^7 rs 



FIRST SERIES No. 56 JANUARY 1, 1922 

UNIVERSITY OF IOWA 
STUDIES 



STUDIES IN CHILD WELFARE 

VOLUM^ II NUMBER 1 

i. 

MENTAL GROWTH CURVE OF NORMAL AND 
SUPERIOR CHILDREN 

STUDIED BY MEANS OF CONSECUTIVE 
INTELLIGENCE EXAMINATIONS 



BY 

Bird T. Baldwin 

AND 
LORLE I. StECHER 



PUBLISHED BY THE UNIVERSITY, IOWA CITY 

Issued semi-monthly throughout the year. Entered at the post office at Iowa City, 
Iowa, as second class matter. Acceptance for mailing at special rate of postage 
provided for in section 1103, Act of October 3, 1017, authorized on July 3, 1918 



Wowffiril 



UNIVERSITY OF IOWA STUDIES 
IN CHILD WELFARE 

Professor Bird T. Baldwin, Ph. D., Editor 



FROM THE IOWA CHILD WELFARE RESEARCH STATION 

VOLUME II NUMBER 1 

MENTAL GROWTH CURVE OF 

NORMAL AND SUPERIOR 

CHILDREN 

STUDIED BY MEANS OF CONSECUTIVE 
INTELLIGENCE EXAMINATIONS 

BYv' 

Bird T. Baldwin 

AND 

LoRLE I. StechEr 



PUBLISHED BY THE UNIVERSITY, IOWA CITY 



■■.'l\ 



LIBRARY OF CONGRESS \ 

RECEIVED i 

JUN7 1922 I 



CONTENTS 



[. The Mental Growth Curve 

1. Statement of the Problem ^ 

2. Data for this study ^ 

Chart I. Typical Record Card for Successive Examinations. 6 

3. Method of Determining the Mental Growth Curve 8 

4. The Analysis of the Mental Growth Curve 10 

Table I. Mean Mental Age in Months of Superior and Aver- 
age Boys and Girls for Successive Chronological Ages 10 

Chart II. Mental Growth Curves for Superior and Aver- 
age Children 

Chart III. Growth Curves in Height 13 

Table II. Mean Intelligence Quotients of Superior and Aver- 
age Boys and Girls for Successive Chronological Ages 14 

5. The Analysis of the I. Q. Curve 14 

6. The Analysis of the Curve of the Rate of Mental Growth 15 
Chart IV. I. Q. Curves of Superior and Average Children.. 15 
Table III. Mean Rate of Mental Growth of Superior and 

Average Boys and Girls for Chronological Age Intervals.. 15 
Chart V. Rate of Mental Growth for Superior and Average 

Children ^^ 

7. Mean Group Differences at Successive Examinations 17 

8. Discussion and Literature 1^ 

Table IV. Mean Intelligence Quotients at Successive Ex- 

aminations ^° 

Table V. Mean Chronological Age and Mean Interval be- 
tween Successive Examinations 19 

9. Summary and Conclusions 22 

II. The Possibh^ity of Prediction of Mental Growth 23 

1. Intelligence Status of Individuals at Successive Examina- 
tions 2^ 

Table VI. Original Data Arranged in Order of Mean I. Q. 

—Boys 24 

Table VII. Original Data Arranged in Order of Mean I. Q. 

—Girls ^^ 

2. Deviation of Individuals from their Mean I. Q. Level 36 

Chart Vla-VIb Successive I. Q.'s 36, 37 

Table VIII. Mean Individual Deviations from Intelligence 

Quotient Level 37 

Chart VII. Individual I. Q. Curves for Boys 38 

Chart VIII. Individual I. Q. Curves for Girls 38 



4 CONTENTS 

3. Differences in I. Q. at Successive Examinations 39 

Table IX. Percentage Distribution of the Differences in 

Intelligence Quotients 40 

Chart IX. Percentage Distribution of the Differences in 
I- Q 41 

4. Intercorrelations 43 

Table X. Intercorrelations of Intelligence Quotient's, for 

Two, Three, Four, and Five Examination Groups 45 

Table XI. Percentage of Children Tested by Same Examiner 45 

5. The Probable Error of Estimate 46 

Table XII. Differences between the Obtained and Predicted 

Intelligence Quotients on Second, Third, Fourth, and 

Fifth Examinations 47 

Table XIII. Distribution of Differences between Obtained 

and Predicted I. Q.'s 48 

Chart X: Distribution of Differences between Obtained and 

Predicted I. Q.'s 49 

6. Summary and Conclusions 52 

III. The Relation between^ Physical and Mental Growth 53 

1. Data 53 

2. Resemblances in the Mental and Physical Development of 
Brothers and Sisters 53 

Chart XI. Individual Mental Growth Curves of Brothers and 
Sisters 54 

3. Mean Mental Age of Physiologically Accelerated and Re- 

tarded Children 55 

Chart XIV. Mean Mental Age in Months of Physiologically 

Accelerated and Retarded Boys and Girls 55 

4. The Relation between Physical Traits and Mental Age 56 

Table XV. Intercorrelations between Physical Traits, Chron- 
ological and Mental Age 57 

Table XVI. Partial Correlations between Physical Traits, 

Chronological and Mental Age 57 

5. Summary and Conclusions 58 

IV. General Conclusions 58 

References 60 



MENTAL GROWTH CURVE OF NORMAL 
AND SUPERIOR CHILDREN 

I. THE MENTAL GROWTH CURVE 

1. Statement of the Prohlem. Contemporary discussions of 
the mental growth curve have their parallel in the early history 
of anthropometry, when scientists attempted to find the general 
laws of growth and to depict the trend of the average curve of 
physical development. Refinement of technique and a better 
analysis of the growth process have showai wide individual dif- 
ferences in the growth of children, which make it impossible to 
represent these variations adequately by a single mean curve. It 
is now known that there are differences in the curves for boys 
and girls, for tall and short children, for physiologically accel- 
erated and retarded children, as well as for children of different 
race, different environment, and different social status. 

On the analogy of the physical growth curve a number of 
writers have constructed theoretical mental growth curves, gen- 
erally with rather a steep rise in the early years of life and a 
flattening out after the age of puberty. One author has suggested, 
without experimental data, that this curve should really be con- 
cave in the early years, owning to what he believes to be the slow 
rate of development during infancy. The concept of different 
rates of development in the subnormal classes has become so 
firmly established that text-books generally visualize for the 
student the supposed growth curves of the three classical levels 
of feeblemindedness. It has also been suggested in the literature 
that superior children grow at a faster rate and have a steeper 
curve than the average. 

All of these problems concerning the general trend of the 
growth curve, the rate of improvement of children of different 
intellectual ability, variability in mental development, the pos- 
sibility of prediction in mental growth, and the relation between 
physical and mental gro^vth can be solved only through a study 
of consecutive re-examinations and observations of the same group 
of children throughout a number of years. The data of this study 



6 IOWA STUDIES IN CHILD WELFARE 

furnish the basis for the beginning of an empirical determination 
of these aspects of the mental growth process. 

2. Data for this Sttidy. In September, 1917, several hundred 
children were examined at the Iowa Child Welfare Research Sta- 
tion by the Stanford Revision of the Binet Scale, with a view to 
following the mental development of the children from year to 
year.^ The continuity of the work was interrupted by war con- 
ditions' and by the shifting^* of the school population particularly 
characteristic of a university town, but 143 individual records are 
sufficiently complete for the purposes of this analysis. Chart I 

CHART I 

TYPICAL RECORD CARD FOR SUCCESSIVE EXAMINA- 
TIONS. 



Nan/IE Hc^'^y^^, K a;tUvv^ Date or Birtm7-i2-^'1 



Date: or EIxam.- I u-^-i? Z ni\?/ii Z) n/f/ig 4 n/"/to ^sjijl 



<^t'^s ,<\\'\.:> 




'During the first year the Yerkes-Bridges Point Scale was given at the same time 
as the Stanford Revision, or a day later. Although this study is limited to the data 
from the Stanford Revision, the Pearson coefficient of correlation between the ratings 
by the two scales, all of the examinations being made by the same individual, was found 
to be for 76 cases +.888 with a P.F.. of ±.016. 

'^he original plan for the re-examinations had the support of the Acting Director 
of the Child Welfare Research Station, Ellsworth Faris, during the Director's absence 
in military service. 

^A number of children who had left the university school were followed up and 
examined in the public schools. A fifth examination on one girl was obtained through 
the courtesy of Professor L. W. Cole, who examined her in Colorado Springs. 



MENTAL GROWTH CURVE 7 

shows a typical record for successive examinations. The records 
may be divided into four groups: (a) 56 having two examina- 
tions; (b) 51 additional cases having three examinations; (c) 42 
of the three examination cases on whom a fourth examination 
was obtained; (d) additional 36 cases having five consecutive ex- 
aminations. 

The conditions for a study of this kind were particularly favor- 
able. The University Observational Schools, in the same building 
as the Child Welfare Research Station, are attended largely by 
the children of the professional and business men of the city and 
of prosperous farmers nearby. The tuition is small, making the 
expense comparable to that of children attending the public 
schools of the town where text-books are not supplied. The tone 
of the school is free and democratic. The children are accustomed 
to all sorts of educational and psychological experiments and re- 
gard the annual re-examination as a regular part of the school pro- 
gram. There is no reason to believe that any undue amount of 
communication or discussion went on among the children in re- 
gard to the mental tests; in fact, the examiner frequently noted 
the fact that a child remembered having been asked a certain 
question a year ago but did not give further evidence that the 
answer had been learned. The investigation had the interest and 
support of the school staff, most of whom were college graduates 
who were anxious to make the experimental conditions as favor- 
able as possible. 

The examinations were given by four psychologists^ during the 
period between September, 1917, and May, 1921. In all 485 
mental age determinations were made on 143 children. Of these 
178 were given by Miss Vest, 8 by Miss Schriefer (who was de- 
voting her time to the examination of other children entering the 
school), 77 by Miss Wagoner, and 222 by Miss Stecher. 

With a view to tracing the possible effect of the personal equa- 
tion, the material was arranged (Table XI) so as to show what 
proportion of the children in a given group were examined by 
the same examiner.- In the 'Fixe Examination Group both the 
first and second examinations were made by Miss Vest in 91.4% 
of the cases; in the Four Examination Group Miss Vest gave 30.2% 
of the repeated examinations, in the Three Examination Group 



^Eloise Vest, A. M., Louise Schriefer, A. M., Lovisa Wagoner, A. M., Lorle I. Stecher, 
Ph. D. 

^In the statistical treatment of the data in this study the writers had the cooperation 
of Gladys M. Fairbanks, A. M. 



8 IOWA STUDIES IN CHILD WELFARE 

22.2%, and in the Two Examination Group 28.6%. Consecutive 
examinations of the same children were given by Miss Stecher 
as follows: in the Two Examination Group 3.5% of the first and 
second; in the Four Examination Group 18.6% of the second and 
third, 18.6% of the second and fourth, 100% of the third and 
fourth; in the Five Examination Group 40% of the third and 
fourth, 40% of the third and fifth, 100% of the fourth and fifth. 
That re-examination by the same person is of practically no sig- 
nificance in raising the correlation is shown in connection with the 
coefficients of correlation on page 45. 

The subjects of the study were of average and superior intel- 
ligence with a range of I. Q. from 90 to 167. The four groups 
were nearly equal in mental ability as shown by the mean I. Q. 
of the boys and girls of the different groups. 



Group 


5 Exam. 


4 Exam. 


3 Exam. 


2 Exam, 


Boys 


120.6 


114.0 


112.8 


115.0 


Girls 


118.8 


113.6 


112.3 


113.4 



It will be noted that the mental ability of the boys was prac- 
tically the same as that of the girls. 

3. Method of Determining the Mental Growth Curve. Terman 
(26) 1919, p. 127, has stated that "the standardization of the 
Binet scale on the basis of age norms makes it a valuable instru- 
ment for the investigation of mental growth curves." The mental 
growth curves presented herewith are probably the first curves 
for superior and average children of the development of general 
intelligence studied by means of repeated examinations on the 
same children. 

The mental examinations on which these growth curves are based 
were made at irregular intervals, ranging on the average from 
6 to 16 months within the period of four years. In order to plot 
the curve at the customary one-year intervals, the mental ages, 
instead of being assigned to the year nearest the chronological 
age, as is the usual custom, were calculated and weighted in such 
a manner as to give the mental age at exact years. This method 
assumes that the child continues to grow mentally at the same 
rate between the examination intervals. A child actually meas- 
ured at the age of 5 years-5 months would, under the usual 
method, be considered as five years and its mental age averaged 
with the mental age of other children who might actually have 
varied between 4 years-7 months and 5 years-6 months at the time 
of the examination. To prevent this distortion of the real age, 



MENTAL GROWTH CURVE 9 

mental and chronological, a new mental age was computed for 
each chronological age during the period of measurement. The 
method used was as follows : 

For each child the difference between every two successive 
chronological ages and every two successive mental ages was cal- 
culated and the rate of improvement obtained by dividing the 
difference in mental age by the difference in chronological age. 
For example, take the case of a boy who had his second examina- 
tion at the age of 6 years-1 month, and his third examination at 
the age of 7 years-2 months, giving a difference in chronological 
age of 13 months. His mental age at the earlier examination was 
8 years-8 months, and at the later, 10 years-2 months, the differ- 
ence in mental age being 18 mental months. The mental age 
difference divided by the chronological age difference results in 
a rate of improvement of 1.38. This means that he grew 1.38 
mental months for every month of chronological age. The mental 
age at the time of the earlier examination was then corrected by 
subtracting from the mental age of 8 years-8 months, or 104 
mental months, the number of mental months equivalent to one 
month's growth at the rate of 1.33 (which is the rate at which 
he was growing previous to 6-1). This gives a new mental age 
at 6 years of 104 mental months — 1.33 mental months, or 102.67 
mental months. The corrected mental age at 6 years was 102.67 
months. The corrected mental age at 7 will be the mental age 
at 6 years-1 month, -|-11 months at the rate of 1.38, or 102.67-}- 
(11X1.38) or 117.85 mental months. 

The resultant mental ages were averaged for each chronological 
age from 5 to 14 for all of the boys and all of the girls of the 
group and for the normal and superior boys and girls separately. 
The resultant mental growth curve is shown in Table I and 
Chart II. 

The rates of growth used for correcting the mental ages from 
the exact year to year by the method of monthly rates described 
above were averaged by chronological age groups to give the 
total growth of each child for all year intervals. The resultant 
composite rates were averaged for each year interval to obtain 
the annual rate of growth. The corrected mental ages were then 
divided by the chronological ages at the exact years in order to 
determine the new rate of improvement between every two suc- 
cessive mental ages. These new rates were averaged by years to 
give the rate of mental growth shown in Table III and Chart V. 



10 



IOWA STUDIES IN CHILD WELFARE 



The new I. Q.'s for each exact chronological age were averaged 
to give Chart IV and Table II. 

4. The Analysis of the Mental Growth Curve. The mental 
growth curves obtained by the individualizing method from con- 
secutive measurements of superior and average boys and girls be- 
tween the ages 5 to 14 present at first glance the appearance of 
a straight line. The familiar parabolic character of the theoret- 
ical growth curve is lacking, since our data furnish us no de- 
terminations for ages 14 to 16, during which this slowing up of 
mental growth is supposed to take place. 





TABLE I 




Melvn Mentax 


Age in Months of Superior and Average Boys and 


Girls for Successive Chronological Ages 




(Based on 487 Consecutive Examinations) 






Boys 


Girls 


Intelligence 


Intelligence 


Intelligence 


Intelligence 


CTironological 


Quotient 


Quotient 


Quotient 


Quotient 


Age 


110 + 


90-110 


110 + 


90-110 




( Superior) 


(Average) 


(Superior) 


(Average) 


5 


70.6 


60.7 


72.0 


62.5 


6 


88.7 


75.6 


85.0 


73.9 


7 


102.2 


87.4 


102.2 


88.9 


8 


118.7 


100.4 


116.3 


100.9 


9 


131.4 


109.2 


131.1 


112.9 


10 


144.0 


117.7 


145.5 


122.4 


11 


160.5 


130.5 


158.5 


133.3 


12 


181.0 


143.1 


184.1 


141.5 


13 


190.0 


157.2 


196.0 


166.5 


14 


208.9 


168.0 


201.0 


182.9 



It is apparent from these curves that superior and average chil- 
dren develop at different levels and that children of these dif- 
ferent intellectual levels grow increasingly dissimilar with in- 
crease in chronological age. For example, at the age of 5 the 
superior and average boys have a mental age of 71 and 61 mental 
months respectively, but at 14 the superior have 209 and the aver- 
age 168. The difference of 10 points at 5 years has increased to 
41 points at 14 years. The girls show similar differences. 

This divergence in the growth curves of average and superior 
children has long been assumed as probable but has not heretofore 
been empirically demonstrated. The concept of the I. Q. pre- 



zao 



MENTAL GROWTH CURVE 
CHART II 



11 




5 6 7 6 9 10 II IZ 
dhronologicpl Age in Year5 

supposes a certain divergence in the curves of the superior and 
the average child, as the superior child has to grow at a rate 
greater than one mental month for one chronological month in 
order to maintain a constant I. Q. 



12 IOWA STUDIES IN CHILD WELFARE 

The general straight line appearance previously noted is espe- 
cially apparent in the growth curve for boys. Further analysis 
reveals, however, a very significant change in the trend with the 
approach of adolescence. This is especially marked in the curve 
for girls where there is a rise in mental development in the supe- 
rior girls between the ages 11 to 12 and in the average girls a year 
later, between the ages 12 to 13. The superior boys show a similar 
acceleration in mental growth at about 12 — somewhat later than 
in the ease of the superior girls. The boys of average mental 
ability have not yet shown this acceleration up to 14 years, which 
is the latest age for which we have a sufficient number of cases. 
It seems unlikely that this rise in the curve of mental growth can 
be explained by defects in the measuring scale at the adolescent 
ages. There is no reason to believe that the scale was not equally 
well standardized at all ages. The increased incline of the curve 
extends, moreover, through several ages, and it is not probable 
that the tests Avould be too easy throughout these years. 

The mental growth curves of the boys and girls cross repeat- 
edly. There is, however, a tendency in the earlier ages for the 
average girls to be a little higher in mental age than the average 
boys, in the later ages for the girls of both groups to be a little 
superior to the boys. While not without exception, this adoles- 
cent superiority of girls is in accordance with other facts indica- 
tive of the earlier maturity of girls. 

There has been in recent years a movement to discredit charac- 
teristic changes in intellectual traits as a result of adolescence. 
This point of view, which is probably a reaction to undue senti- 
mental emphasis of those changes current in the psychology of 
twenty years ago, is expressed by Terman (25) 1917, p. 60, who 
maintains there is little evidence of periodicity, or irregularity 
as far as general intelligence is concerned, and throws doubt on the 
existence of the adolescent spurt. Although there is obviously no 
time in the mental development of the child when new mental 
traits suddenly appear, the rise in the mental growth curves ap- 
parent at the ages of 11 to 14 may be attributed to increased 
strength of traits that have long been developing, or to increased 
mental vigor similar to the accelerated growth in physical traits. 
The existence of such a period of increased vigor would not 
necessarily interfere with the stability of the I. Q., providing the 
scale was adapted in difficulty to such a change. It certainly 
would not affect the individual's position in the group relative 



MENTAL GROWTH CURVE 



13 



CHART III 




to a norm, since the norm at these ages would also be higher if 
all children developed in a similar way. A child's physical status 
in height, for example, remains relatively constant with reference 
to its group from age 6 through adolescence, as sliovni by Baldwin 
(1) 1914, though the norms and individual curves may show 
adolescent accelerations. 

The mental growth curves are strikingly similar to the physical 
growth curves in height as shown in Chart III. This chart here 
published for the first time illustrates the differences in the 
growth of tali, average and short girls and of a tall and a short 



14 



IOWA STUDIES IN CHILD WELFARE 



boy as compared with the norms for boys and girls. The norms 
for average boys and girls are based on 6 to 10 years of semi- 
annual measurements for 60 boys and 60 girls. The curves for 
tall girls are based on similar material for 52 cases distributed 
above the norm, and the curves for short girls on 28 cases con- 
siderably below the norm. The curves show the same phenomena 
that have been pointed out in connection with the mental growth 
curves. In both cases the curve at the higher level shows the 
acceleration at an earlier age. 



TABLE II 

Mean Intelligence Quotients of Superior and Average Boys and 

GiBLS FOR Successive Chronological Ages 


Chronological 
Age 


Boys 


Girls 


Intelligence 
Quotient 

110 + 
Superior 


Intelligence 
Quotient 

90-110 
Average 


Intelligence 
Quotient 

110 + 
Superior 


Intelligence 
Quotient 

90-110 
Average 


5 

6 

7 

8 

9 

10 

11 

12 

13 

14 


117.6 
123.3 
121.6 
123.6 
121.7 
119.9 
121.5 
125.7 
121.5 
124.3 


101.2 

105.0 

104.0 

104.6 

101.1 

98.1 

98.8 

99.4 

100.8 

100.0 


119.9 
118.0 
121.7 
121.1 
120'.5 
120.3 
119.8 
127.9 
125.7 
119.7 


104.1 
102.6 
105.9 
105.1 
It)4.6 
102.1 
99.9 
98.2 
106.7 
108.9 



5. The Analysis of the I. Q. Curve. The mean intelligence 
quotients (Table II) and the I. Q. curves (Chart IV) for superior 
and average boys and girls show some of the same characteristics 
observed in the mental growth curves. The curves are in general 
approximately horizontal, confirming within limitations the con- 
stancy of the I. Q. There appear to be, however, certain definite 
phenomena associated with physiological development that show 
themselves in a decrease or increase in the I. Q. at certain chrono- 
logical ages, A study of the physical development of young chil- 
dren shows that there is considerable fluctuation between the 
ages 4 and 7. These I. Q. curves suggest a similar condition with 
a small spurt in mental development, appearing a little later in 
the boys than in the girls. Both superior boys and girls shoAV 
a rise in the I. Q. between the ages of 11 and 12. Average girls 



MENTAL GROWTH CURVE 



15 



CHART IV 




7 a 9 10 

Age in Yeorg 

also show this adolescent acceleration, although it appears a year 
later than in the case of superior girls. The I. Q. curve and the 
mental growth curve of the average boys do not show this phe- 
nomenon, possibly because they have not reached this stage of 
acceleration. 

6. The Analysis of the Curve of the Rate of Mental Growth. 
Our tables of original data do not include calculations of the 
actual number of mental months growth for one chronological 
month between examinations, although these were used in all 



TABLE III 
Mean Rate of Mental Gbowth of Superior and Average Boys and 
Girls for Chronological Age Intervals 


Chronological 

Age 

Intervals 


Boys 


Girls 


Intelligence 
Quotient 

110 + 
Superior 


Intelligence 
Quotient 

90-110 
Average 


Intelligence 
Quotient 

110 + 
Superior 


Intelligence 
Quotient 

90-110 
Average 


5-6 

6-7 

7-8 

8-9 

9-10 

10^11 

11-12 

12-13 

13-14 


1.5 

1.2 
1.5 
1.4 
1.4 
1.8 
1.8 
(1.1) 
1.5 


1.0 
1.1 
1.2 
1.3 
1.0 
1.1 
1.3 
1.3 
1.1 


1.2 
1.5 
1.2 
1.3 
1.5 
1.6 
2.2 
1.9 
1.9 


.8 
1.1 
1.1 
1.2 

.8 
1.1 
1.1 
1.6 
1.4 



16 



IOWA STUDIES IN CHILD WELFARE 



cases as a basis for the curve of the rate of mental growth. In- 
spection of the tables will show for individual children great 
fluctuation in the rate from examination to examination. A child 
whose rate from the first to the second examination is 1.56 mental 
months for each month of chronological age may show between 
the second and third examination a rate of .23 mental months 
for each chronological month. Part of this discrepancy is of 
course due to the experimental error of each single mental age 
determination, but the size of many of the irregularities cannot 
be explained on this basis. It appears that there is no rate of 
improvement which is characteristic of the individual and uni- 
formly maintained throughout his years of mental growth al- 
though an approximately constant rate is maintained in many 
cases. 

Table III and Chart V show the mean rate of mental growth 
for these children. The average children grow approximately 

CHART V 




Cnronoiogtcol A^e tnfert/aii> 



one mental month for each chronological month, while the supe- 
rior children have a higher rate (shown by the curve at a higher 
level) except in the case of boys between 12 and 13, where the 
small number of cases results in a decreased rate (printed in 
parenthesis in Table III and represented by a dotted line in Chart 
V). The effect may also be noted in the mental growth curve 
for superior boys, Chart I. 

There is little difference, on the average, in the rate of growth 
of these two groups of children. In no case is the difference 



MENTAL GROWTH CURVE 17 

greater than seven-tenths of a year. These figures cannot of 
course be considered as norms, since they depend upon the selec- 
tion of cases included in the study. The addition of more cases of 
very superior intelligence, or of more cases of I. Q.'s below 100 
would have increased the difference. 

The general prepubertal increase in mental development be- 
comes evident earlier in the case of superior children than in 
average children, and in the case of superior girls about a year 
earlier than in average boys. In comparing the curves it should 
be kept in mind that a child who has been growing at a certain 
rate and then reaches a period of little or no increase will have 
to reattain the rate of growth at which he was previously de- 
veloping before an actual acceleration in growth can be consid- 
ered as taking place. The period of acceleration is therefore later 
than the point in the curve at which the steep rise begins. In 
general all of these curves show less difference between average 
and superior boys in regard to these adolescent phenomena than 
between average and superior girls, who are usually a year apart 
in their general development. 

Our data do not permit us to give a definite answer to the ques- 
tion whether superior children grow more superior as time goes 
on through an increase in the rate of mental growth. The curves 
for the two groups of children seem to diverge slightly at the 
higher ages, especially in the case of girls at the adolescent years. 
The facts in regard to the change of I. Q. to be reported later on 
page . . seem also to indicate some characteristic differences in 
the growth of children of different I. Q. level. We should hesi- 
tate, however, to make any generalization in regard to this matter 
from the material presented in this study. 

7. Mean Group Differences at Successive Examinations. Table 
V is purely descriptive, presenting the mean chronological age 
at successive examinations and the mean interval between exam- 
inations for use in interpreting the findings in other tables. The 
findings of Table IV are averages of the I. Q.'s obtained at each 
examination by the children of each particular group. 

It is a very significant fact that the mean I. Q. of each of the 
four groups of children increased with each successive examina- 
tion, which must be regarded as an effect of greater habituation 
or practice. The increase in the mean I. Q. is proportionate to 
the number of re-examinations. 



18 



IOWA STUDIES IN CHILD WELFARE 



The mean I. Q. for the Five Examination Group increased from 
115.39 through 119.5, 119.75 and 123.91 to 126.7. The mean I. Q. 
for the Four Examination Group increased from 111.06 through 

112.02 and 115.16 to 118.20. The mean I. Q. for the Three Ex- 
amination Group increased from 110.59 through 111.80 to 115.21. 
The mean I. Q. for the Two Examination Group increased from 

112.3 to 115.8. This increase in I. Q. has been noted by previous 
workers on a single retest in the summary by Rugg and CoU- 
oton (21). 



TABLE IV 
Mean Intelligence Quotients at Successfve Examinations 



Group 



No. of 










Cases 


Exam. 1 


Exam. 2 


Exam. 3 


Exam. 4 


36 


115.4 


119.5 


119.8 


123.9 


42 


111.1 


112.0 


115.2 


118.2 


51 


110.6 


111.8 


115.2 




56 


112.3 


115.8 







Exam. 5 
126.7 



There is also an increase in the mean rate of improvement upon 
successive examinations. To investigate this phase of the practice 
effect, the data for the Four and the Five Examination Groups 
were worked over to give for each child the amount of increase 
in mental age months for each month of chronological age in- 
crease between the first and second examination, the second and 
third and the third and fourth. The means of these individual 
rates of improvement reveal a general increase in the rate of 
mental development which is especially marked between the third 
and fourth examination in the case of the girls. 



mination 




III 


II-III 


III-IV 




No. cases 


Eate 


Eate 


Eate 


Boys 


37 


1.48 


1.42 


1.73 


Girls 


34 


1.29 


1.64 


2.40 



8. Discussion and Literature. It is extremely probable that 
the theoretical mental growth curves found in so many text- 
books really misrepresent the facts of mental development. It 
has been the custom to draw the growth curves of children of 
different degrees of ability as if all of these curves began with 
zero ability at the time of birth and from that time on rose 
steadily. From all that we know in regard to differences in the 
mental capacity of young children, the cur^^es of mental develop- 
ment, like the curves of physical development, begin at dif- 



MENTAL GROWTH CURVE 



19 







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ferent levels (points). 
There are individual men- 
tal differences at birth as 
there are individual dif- 
ferences in height. It is 
not conceivable that the 
feebleminded child should 
begin at the same point 
with the child of average 
or superior ability and 
then drop back in the race 
as his more gifted brothers 
gain. The truth of the 
matter is, he runs on a 
relatively lower level 
throughout life. 

Much of the work on 
retests of children has 
been done with feeble- 
minded subjects. While it 
is impossible in this study 
on normal and superior 
children to go into the 
question of growth curves 
of the feebleminded, it 
will orientate the problem 
if we review briefly such 
other studies as have been 
made with repeated exam- 
inations. Bobertag (6) p. 
528, reported in 1912 as a 
result of retests on 83 
children whom he had ex- 
amined the year before 
that children whose intel- 
ligence is above average 
advance more rapidly ; 
those whose intelligence is 
below average advance 
more slowly. He main- 
tained (p. 531) that if one 



20 IOWA STUDIES IN CHILD WELFARE 

limits one's self to a few successive years — 8, 9, 10, for example — 
one could say that the I. Q. is approximately constant. If, how- 
ever, one considers all the ages, or the whole developmental course 
of children's intelligence it is very questionable whether the as- 
sumption of a constant I. Q. is tenable. 

Berry (4) in 1913 found on a retest of 82 children that the 
normal subjects made an average gain of 1 year, and the feeble- 
minded — mental ages 4-11 years — an average gain of .5 of a year. 
He did not report the correlation between the examinations. 

Bloch (5) 1915 re-examined defective children by the Binet 
scale. 

Stern (23) (24) 1914 and 1916, who discussed the subject at 
length, but without experimental data of his own, believed that 
the I. Q. did not afford an actually constant expression of degree 
of feeblemindedness but showed a tendency to fall in value as 
chronological age increased and the age of arrest was approached. 

Descoeudres (9) 1915 retested 26 children of a special class 
and found the I. Q. very similar to the previous one with a greater 
tendency to increase. Cases with three or four examinations 
showed practically the same I. Q. with less than 50% variation. 

Terman (25) p. 55, 1917 concluded from re-examinations that 
"the results of 140 such tests show as far as the age of 13 or 14, 
even when the tests are separated by as much as five years, 
changes of 10 points in 12 are relatively rare. In general, it can 
be said that the superior children of the first test are found supe- 
rior in the second, the average remained average, the inferior 
remain inferior, the feebleminded remain feebleminded and nearly 
always in approximately the same degree. The most marked ex- 
ceptions to this rule are found with the feebleminded whose in- 
telligence quotient shows a tendency to decrease considerably." 

Cuneo and Terman (8) 1918, retested 77 children and found 
high correlations between the two tests. 

Terman (26) 1919 found considerable agreement in the I. Q.'s 
of 46 children tested three or more times. He says, p. 147: "It 
is possible that feebleminded children testing below 60 are less 
likely to hold their own than those of milder degree of defect. 
. . . On the other hand the I. Q. as determined by the Stanf ord- 
Binet (or any other intelligence scale yet devised) cannot indef- 
initely hold its constanc}^ in the case of children who are excep- 
tionally superior. ' ' 



MENTAL GROWTH CURVE 21 

Wallin (28) 1919 discussed the use of the I. Q. in classification 
without data from retests. His article has been critically re- 
viewed by Rosenow (20) 1920, who presents experimental evi- 
dence of approximate stability of the I. Q. from retests of 69 
cases examined at about 10 months interval. 

Wallin (29) 1921 reported re-examinations on 153 children by 
different revisions of the Binet tests. 

Kuhlmann (17) (18) who had discussed the intelligence of the 
feeble-minded is also reported by Hollingworth (15) p. 105 in 1920 
to have found that "On the whole the I. Q. for a given case remains 
constant with a slight tendency on the average to decrease after 
the ages of about nine or ten. ' ' 

Kuhlmann (18a) 1921 reported results on 639 cases ranging from 
idiocy to nearly normal mentality examined 2 to 5 times within a 
10 year period by the Binet and Kulilmann series. He found that 
the I. Q. decreased with age and more for the higher than for the 
lower grades. 

Garrison (13) 1921 retested by the Stanford-Binet 94 children 
who had previously been tested by the Goddard Revision and 
found on the whole, a rather close correspondence. 

Doll (10) 1921, from a study of numerous growth curves for 
feebleminded subjects who had received at least 5 annual exam- 
inations, believes in an age of arrest for the feebleminded beyond 
which the I. Q. would decrease. Terman (27) 1921 criticizes this 
presentation and the conclusion drawn from the data. 

Freeman (12) 1921, published an important discussion on the 
concept of the I. Q. with reference to age scales and point scales. 

Rugg and Colloton (21) 1921, have assembled the reports of 
other workers with Stanford-Binet tests and added data from 137 
cases of their own. They find that with one exception investiga- 
tors have found an average difference in I. Q. on re-examination of 
4.5 points, and confirm in some other respects Terman 's 1917 con- 
clusions. 

The literature summarized above presents many interesting 
problems in regard to the age of arrest or the limit of mental 
growth. Our data do not extend far enough to permit us to spec- 
ulate on the age at which mental growth ceases in the normal or 
superior child, though there is reason to suspect that the mental 
age curves of some of the superior girls are beginning to flatten 
out with a resulting decrease in I. Q. Even so this may be merely 



22 IOWA STUDIES IN CHILD WELFARE 

a fictitious slowing up of mental growth due to the inevitable 
"bumping" into the upper limit of the scale. 

Summary and Conclusions 

1. The fundamental problems concerning the general trend of 
the growth curve, the rate of improvement of children of different 
intellectual ability, variability in mental development, the pos- 
sibility of prediction in mental growth and the relation between 
physical and mental growth can be solved only through a study 
of consecutive reexaminations and observations of the same group 
of children throughout a number of years. 

2. The mental growth curves presented herewith are probably 
the first curves for superior and average children of the develop- 
ment of general intelligence studied by means of repeated exam- 
inations on the same children. 

3. The curves constructed from the corrected mental age rat- 
ings do not misrepresent the actual growth process as is the case 
when the chronological age is approximated to the nearest year. 

4. It is apparent from these curves that superior and average 
children develop at different levels and that children of these dif- 
ferent intellectual levels grow increasingly dissimilar in mental 
age with increase in chronological age. This divergence in the 
growth curves of average and superior children has long been 
assumed as probable but has not heretofore been empirically 
demonstrated. 

5. An analysis of the mental growth curve reveals a significant 
change in the trend with the approach of adolescence, which ap- 
pears earlier in the case of superior children. There is also an 
adolescent superiority of girls which is in accordance with other 
facts indicative of the earlier maturity of girls. 

6. The mental growth curves are strikingly similar to the 
physical growth curves in height. 

7. The I. Q. curves are approximately horizontal, confirming 
within limitations the constancy of the I. Q. There are fluctua- 
tions associated with physical development. 

8. The curves of the rate of mental growth are higher for 
superior than for average children, and seem to diverge slightly 
at the adolescent years. 

9. The general prepubertal increase appears earlier in the case 
of superior children. 



MENTAL GROWTH CURVE 23 

10. The mean I. Q. of each of the four groups of children in- 
creased with each successive examination, which is probably an 
effect of greater habituation or practice. 

11. There is also an increase in the mean rate of improvement 
on successive examinations. 

II. THE POSSIBILITY OF PREDICTION IN MENTAL 

GROWTH 

1. Intelligence Status of Individuals at Successive Examina- 
iions. The stability of the I. Q. is one of the most important prob- 
lems under discussion by psychologists at the present time. Upon 
the relative stability of the ratio between mental and chronolog- 
ical age depends to a large extent the possibility of prediction in 
mental growth. 

Binet and Simon felt very doubtful of the possibility of using 
the I. Q. for prediction. Even Bobertag (5) and Stern (24), who 
are among the earliest advocates of the use of the I. Q., did not 
believe that it would remain constant for later ages. 

The question of the stability of the I. Q. has been discussed in 
a number of theoretical articles. Some writers believe that it re- 
mains practically constant and others have found a tendency for 
the I. Q. of the feebleminded to decrease and for the I. Q. of the 
superior to increase. Any conclusive answer to the question of 
whether the I. Q. remains constant depends upon the accumula- 
tion of a sufficient number of long-time mental growth curves 
for children of different intellectual capacity. 

Terman (26) 1919, p. 137, states the problem briefly thus: "By 
applying it [the Binet scale] repeatedly to the same children we 
can find out whether constancy or irregularity rules. Prediction 
hinges on the question whether a child who is found by the test 
to be a given per cent above or below the mental level normal 
for his age continues to be accelerated or retarded to the same 
degree. The answer is found in the extent to which the I. Q. 
remains constant." 

Psychologists who have been accustomed to thinking that aU. 
that was required for a solution of the problems of mental growth 
was the accumulation of a sufficient number of re-examinations 
for long periods will find that the repetition of the intelligence 
scale brings up many puzzling new problems. A study of the 
original data. Tables VI and VII, shows just what variations in 



24 



IOWA STUDIES IN CHILD WELFARE 



TABLE VI 
Original Data Arranged in Oedeb of Mean I. Q. — Boys 



10. 



13. 



Average I. Q. 158.0. 

Examiner E. V. 

Chronological Age 5-3 

Terman Age -— — 8-5 

I. Q 160 

Average I. Q. 150.7. 

Examiner E. V. 

Chronological Age 5-11 

Terman Age 8-5 

I. Q 142 

Average I. Q. 143.6. 

Examiner E. V. 

Chronological Age 5-1 

Terman Age 7-4 

I. Q. - 144 

Average I. Q. 142.6. 

Examiner E. V. 

Chronological Age 8-2 

Terman Age 11-1 

I. Q - 135 

Average I. Q. 138.2. 

Examiner E. V. 

Chronological Age 5-9 

Terman Age 7-6 

I. Q. 132 

Average I. Q. 137. 

Examiner L. W. 

Chronological Age 5-9 

Terman Age 7-8 

I. Q 133 

Average I. Q. 134.5. 

Examiner E. V. 

Chronological Age 6-10 

Terman Age 8-9 

I. Q 128 

Average I. Q. 131.8. 

Examiner E. V. 

Chronological Age 10-7 

Terman Age 12-5 

I. Q. — - 117 

Average I. Q. 129.0. 

Examiner — — L. W. 

Chronological Age 6-1 

Terman Age 7-4 

I. Q - 121 

Average I. Q. 128.0. 

Examiner E. V. 

Chronological Age 6-3 

Terman Age 8-0 

I. Q. - - 128 

Average I. Q. 128.0. 

Examiner E. V. 

Chronological Age 6-1 

Terman Age 7-6 

I. Q 123 

Average I. Q. 127.6. 

Examiner E. V. 

Chronological Age 10-6 

Terman Age 12-8 

I. Q 120 

Average I. Q. 127.2. 

Examiner E. V, 

Chronological Age 7-1 

Terman Age .— 8-6 

I. Q 120 

Average I. Q. 126.0. 

Examiner L. W. 

Chronological Age 7-3 

Terman Age 9-2 

r. Q 126 



E. V. 








5-10 








9-1 








156 








L. W. 


L. I. S. 


L. I. 8. 




7-0 


7-11 


8-6 




9-4 


13-3 


13-9 




133 


167 


161 




E. V. 


L. W. 


L. I. S, 


L. I. S 


6-1 


7-2 


8-1 


8-7 


8-8 


10-2 


11-7 


12-8 


142 


142 


143 


147 


E. V. 


L. W. 


L. I. 8. 


L. I. 8 


9-3 


10-3 


11-2 


11-8 


12-1 


15 


16-11 


17-8 


130 


146 


151 


151 


E. V. 


L. W. 


L. I. S. 


L. I. 8 


6-9 


7-9 


8-8 


9-2 


9-9 


10-3 


11-7 


13-9 


144 


132 


133 


150 


L. I. S. 








6-11 








9-9 








141 








L. W. 








9-2 








12-11 








141 








E. V. 


L. W. 


L. I. 8. 


L. I. 8. 


12-1 


12-7 


13-7 


14-0 


16-8 


17-2 


18-1 


19-0 


136 


137 


133 


136 


L. I. 8. 








7-0 








9^7 








137 








E. V. 


L. I. 8. 


L. I. 8. 




7-4 


9-4 


9-10 




9-4 


11-4 


13^ 




127 


121 


136 




E. V. 


L. I. S. 


L. I. 8. 


L. I. 8. 


7-1 


8-8 


9-1 


9-7 


9-2 


11-3 


11-6 


12-9 


129 


129 


126 


133 


L. S. 


L. I. 8. 


L. I. S. 


L. I. 8. 


12-0 


13-1 


13-6 


14-0 


15-5 


17-0 


17-6 


lS-6 


128 


129 


129 


132 


L. I. S. 


L. I. S. 


L. I. S. 




8-8 


9-1 


9-8 




11-2 


12-1 


12-4 




1^ 


133 


127 




L. I. S. 








8-1 








10-2 








126 









MENTAL GROWTH CURVE 



25 



TABLE VI — Continued 
Original Data Aebanged in Ordeb of Mean I. Q. — Boys 



Average I. Q. 124.5. 

Examiner E. V. 

Chronological Age 9-1 

Terman Age 10-8 

I. Q 117 

Average I. Q. 124.2. 

Examiner E. V. 

Chronological Age 8-4 

Terman Age 10-9 

I. Q 129 

17. Average I. Q. 124.0. 

Examiner E. V. 

Chronological Age 8-3 

Terman Age 10-1 

I. Q. - - 122 

18. Average I. Q. 123.5. 

Examiner L. W. 

Chronological Age - 0-11 

Terman Age 8-8 

I. Q. 125 

19. Average I. Q. 123.5. 

Examiner L. W. 

Chronological Age 8-7 

Terman Age 10-4 

I. Q -- 120 

Average I. Q. 123.0. 

Examiner E. V. 

Chronological Age 10-4 

Terman Age 12-8 

I. Q 122 

21. Average I. Q. 122. 

Examiner E. V. 

Chronological Age 5-4 

Terman Age 6-2 

I. Q 116 

22. Average I. Q. 121.7. 

Examiner — E. V. 

Chronological Age 9-8 

Terman Age 11-4 

I. Q — . 117 

Average I. Q. 121.2. 

Examiner -— E. V. 

Chronological Age 5-2 

Terman Age 5-8 

I. Q 109 

Average I. Q. 121.0. 

Examiner E. V. 

Chronological Age .- 10-9 

Terman Age 11-9 

I. Q. - 109 

25. Average I. Q. 120.8. 

Examiner E. V, 

Chronological Age _ 8-6 

Terman Age 9-11 

I. Q lie 

26. Average I. Q. 120.2. 

Examiner E. V. 

Chronological Age 5-1 

Terman Age 5-10 

I. Q. lU 

27. Average I. Q. 120.0. 

Examiner E. V. 

Chronological Age 9-0 

Terman Age 10-8 

I. Q. - - — 118 

Average I. Q. 120.0. 

Examiner L. W. 

Chronological Age 5-9 

Terman Age 6-6 

1. Q .- — 113 



L. W. 


L. I. S. 


L. I. S. 




10-5 


11-0 


11-7 




12-6 


14-6 


14-11 




120 


132 


129 




L. W. 


L. I. S. 


L. I. S. 




10-4 


11-3 


11-10 




11-10 


14-1 


15-4 




114 


125 


129 




E. V. 


L. W. 


L. I. S. 


L. I. S. 


9-6 


10-6 


11-2 


11-8 


11-11 


13-1 


13-11 


14-7 


125 


124 


124 


125 


L. I. S. 








7-10 








9-7 








122 








L. I. S. 








9-3 








11-9 








127 








E. V. 


L. W. 


L. I. S. 


L. I. S. 


11-11 


12-11 


13-5 


13-10 


15-0 


15-5 


16-3 


16-8 


125 


119 


121 


128 


L. I. S. 








8-3 








10-7 








128 








E. V. 


L. I. S. 


L I. S. 




11-3 


12-9 


18-3 




14-1 


15-3 


16-8 




125 


119 


126 




L. W. 


L. I. S. 


J . I. S. 




6-6 


7-3 


7-10 




7-6 


9-5 


10-4 




115 


129 


132 




E. V. 








12-4 








16-5 








133 








E. V. 


L. W. 


L I. S. 


L. I. S. 


9-7 


10-10 


11-7 


12-0 


11-4 


13-3 


14-4 


14-11 


118 


122 


124 


124 


E. V. 


L. W. 


L I. S. 


L. I. S. 


5-8 


7-0 


7-8 


8^ 


7-0 


7-10 


9-6 


10-8 


1?3 


'11 


124 


129 


E. V. 


L. W. 






10-0 


11-3 






12-1 


i.'j-a 






120 


122 






L. I. S. 








6-6 








8-2 








127 









26 



IOWA STUDIES IN CHILD WELFAKE 



TABLE VI — Continued 
Original Data Arrange^) in Order of Mean I. Q. — Boys 



Average I. Q. 119.7. 

Examiner E. V. 

Chronological Age 9-10 

Terman Age 7-4 

I. Q. 107 

Average I. Q. 119.2. 

Examiner E. V. 

Chronological Age — 5-0 

Terman Age 5-9 

I. Q - 115 

Average I. Q. 119.0. 

Examiner E. V. 

Chronological Age 7-8 

Terman Age 9-2 

I. Q. 120 

Average I. Q. 118.5. 

Examiner E. V. 

Chronological Age 6-0 

Terman Age 8-10 

I. Q. — lU 

Average I. Q. 118.0. 

Examiner E. V. 

Chronological Age 5-3 

Terman Age 6-2 

I. Q. 117 

Average I. Q. 118.0. 

Examiner E. V. 

Chronological Age 10-1 

Terman Age 10-4 

I. Q. 102 

Average I. Q. 117.9. 

Examiner E. V. 

Chronological Age 9-2 

Terman Age -. - 10-3 

I. Q. 112 

Average I. Q. 117.5. 

Examiner L.S.&E.V. 

Chronological Age 11-8 

Terman Age 14-3 

I. Q. 122 

Average I. Q. 117.5. 

Examiner E. V. 

Chronological Age 8-10 

Terman Age 10-4 

I. Q. - 117 

Average I. Q. 117.0. 

Examiner L. W. 

Chronological Age 0-1 

Terman Age 9-10 

I. Q. 112 

Average I. Q. 116.6. 

Examiner E. V. 

Chronological Age 7-9 

Terman Age 9-6 

I. Q. 122 

Average I. Q. 116.5. 

Examiner E. V. 

Chronological Age 8-3 

Terman Age - — 8-11 

I. Q. 108 

Average I. Q. 116.2. 

Examiner E. V. 

Chronological Age 10-2 

Terman Age 11-11 

I. Q. 117 

Average I. Q. 116.0. 

Examiner E. V. 

Chronological Age 8-11 

Terman Age 10-2 

I. Q. lU 



E. V. 


L. I. S. 


L I. S. 




8^ 


9-11 


10-5 




9-4 


12-0 


14-5 




112 


122 


138 




L. W. 


L. I. S. 


L. I. S. 




9-6 


7-2 


7-8 




7-11 


8-7 


9-3 




122 


119 


121 




E. V. 








9-1 








10-6 








118 








L. W. 








7-3 








8-11 








123 








E. V. 


L. W. 


L. I. S. 


L. I. S. 


5-10 


7-2 


7-10 


8-6 


7-0 


8-2 


9-5 


10-1 


120 


114 


120 


119 


E. V. 


L. W. 


L. I. 8. 


L. I. 8. 


11-2 


12-8 


13-2 


13-7 


12-8 


15-5 


16-5 


17-4 


118 


122 


125 


128 


E. V. 


L. W. 


L. I. S. 


L. I. 8 


10-3 


11-5 


12-3 


12-8 


11-11 


14-0 


14-10 


14-10 


119 


122 


121 


117 


L. I. S. 








14-3 








19-2 








113 








E. V. 








9-11 








11-9 








118 








L. r. s. 








6-10 








8-4 








122 








E. V. 


L. W. 


L. I. S. 


L. I. S. 


9-0 


ICM) 


10-8 


11-3 


10-6 


10-9 


12-7 


13-6 


119 


107 


118 


120 


E. V. 


L. I. S. 


L. I. S. 




9-3 


11-4 


11-10 




10-9 


13-3 


14-10 




116 


117 


125 




E. V. 


L. I. S. 


L. r. s. 




11-9 


13-3 


13-9 




14-1 


14-10 


16-1 




119 


112 


117 




E. V. 








9-11 








11-8 








118 









MENTAL GROWTH CURVE 



27 



TABLE VI— Continued 
Oeiginal Data Arranged in Ordi:r of Mean I. 



Q.— Boys 



Average I. Q. 115.5. 

Examiner E. V. 

Chronological Age 6-10 

Terman Age 7-8 

I. Q 112 

Average I. Q. 114.9. 

Examiner E. V. 

Chronological Age 5-t 

Terman Age 5-8 

I. Q 106 

Average I. Q. 113.6. 

E.xaminer E. V. 

Chronological Age ^2 

Terman Age _ 9-8 

I. Q. 105 

Average I. Q. 113.4. 

Examiner E. V. 

Chronological Age 5-0 

Terman Age 5-10 

r. Q. - 106 

47. Average I. Q. 113.0. 

Examiner E. V. 

Chronological Age 8-9 

Terman Age -. 9-7 

I. Q. 109 

48. Average I. Q. 112.7. 

Examiner E. V. 

Chronological Age 11-0 

Terman Age - 11-3 

I. Q. 102 

49. Average I. Q. 111.6. 

Examiner E. V. 

Chronological Age 6-3 

Terman Age 7-2 

I. Q. 114 

50. Average I. Q. 111.5. 

Examiner L. W. 

Chronological Age 7-4 

Terman Age 8-4 

I. Q 113 

Average I. Q. lll.O. 

Examiner M. 

Chronological Age 5-4 

Terman Age 5-8 

I. Q loa 

Average I. Q. 110.5. 

Examiner L. W. 

Chronological Age 7-4 

Terman Age 7-8 

I. Q 105 

Average I. Q. 110.0. 

Examiner E. V. 

Chronological Age 6-8 

Terman Age 7-0 

I. Q. 105 

54. Average I. Q. 110.0. 

Examiner L. W. 

Chronological Age G-l 

Terman Age 7-2 

I. Q. 113 

Average I. Q. 108.7. 

Examiner E. V. 

Chronological Age .- 6-4 

Terman Age 7-0 

I. Q llf) 

Average I. Q. 107.5. 

Examiner E. V. 

Chronological Age 6-2 

Terman Age 6-8 

I. Q. --.. 105 



E. V. 








7-10 








9-4 








119 








E. V. 


L. W. 


L. I. 8. 


L. I. 8 


5-11 


7-3 


7-11 


8-6 


7-0 


8-8 


8-10 


10-4 


118 


117 


111 


121 


E. V. 


L. W. 






10-2 


11-6 






10-10 


15-0 






109 


130 






E. V. 


L. I. 8. 


L. I. S. 


L. I. 8 


0-Q 


8-1 


8-7 


9-1 


7-4 


9-0 


10-2 


10-11 


112 


111 


118 


120 


E. V. 


L. W. 


L. I. S. 


L. I. 8 


9-9 


11-1 


n-8 


12-3 


10-6 


12-« 


13-4 


14-8 


107 


115 


114 


120 


E. V. 


L. r. s. 


L. I. S. 




12-7 


14-1 


14-7 




14-10 


18-8 


16-8 




117 


118 


114 




E. V. 


L. W. 






7-3 


8-7 






8-0 


9-6 






110 


111 






L. I. S. 








8-2 








9-0 








110 








L. I. S. 








6-7 








7-8 








119 








L. I. 8. 








8-6 








9-10 








118 








E. V. 


L. I. 8. 






7-8 


9-3 






8^ 


10-10 






108 


117 






L. I. S. 








7_-> 








7-8 








107 








L. W. 


L. r. s. 


L. r. 8. 




7-10 


8-.) 


8-11 




8-0 


9-2 


10-2 




103 


109 


114 




E. V. 








7-1 








7-10 








110 









28 



IOWA STUDIES IN CHILD WELFARE 



TABLE VI— Continued 
Original Data Arranged in Order of Mean I. Q. — Boys 



70. 



Average I. Q. 106.7. 

Examiner .-. E. V. 

Chronological Age 5-11 

Terman Age 6-2 

I. Q. 104 

Average I. Q. 106.7. 

Examiner E. V. 

Chronological Age 11-0 

Terman Age 12-0 

I. Q. — - 109 

Average I. Q. 106.0. 

Examiner E. V. 

Chronological Age 11-1 

Terman Age 11-6 

I. Q. 104 

Average I. Q. 105.7. 

Examiner — E. V. 

Chronological Age — 11-2 

Terman Age 11-1 

I. Q 9S 

Average I. Q. 105.6. 

Examiner E. V. 

Chronological Age 12-5 

Terman Age 12-2 

I. Q - 97 

Average I. Q. 105.5. 

Examiner E. V. 

Chronological Age 5-4 

Terman Age 5-^ 

I. Q - - 103 

Average I. Q. 105.5. 

Examiner E. V. 

Chronological Age 9-7 

Terman Age — 10-1 

I. Q 105 

Average I. Q. 103.0. 

Examiner E. V. 

Chronological Age 8-8 

Terman Age 9-0 

I. Q. - 104 

Average I. Q. 103.0. 

Examiner L. W. 

Chronological Age 10-4 

Terman Age 10^5 

I. Q. .- 101 

Average I. Q. 102.7. 

Examiner E. V. 

Chronological Age 11-8 

Terman Age 11-7 

I. Q. 99 

Average I. Q. 102.5. 

Examiner E. V. 

Chronological Age 5-5 

Terman Age 5-5 

I. Q - lOO 

Average I. Q. 99.5. 

Examiner E. V. 

Chronological Age 6-7 

Terman Age 6-8 

I. Q. -- - 101 

Average I. Q. 97.5. 

Examiner E. V. 

Chronological Age 7-3 

Terman Age 7-2 

I. Q - 99 

Average I. Q. 97.5. 

Examiner E. V. 

Chronological Age 10-9 

Terman Age 10-8 

I. Q 99 



L. W. 


L. I. 8. 


L. I. 8. 




7-5 


8-1 


8-7 




7-10 


8-8 


9-5 




106 


107 


110 




L. W. 


L. I. 8. 


L. I. 8. 




12-2 


13-0 


13-6 




12-11 


14-1 


14-1 




106 


108 


104 




E. V. 








12-S 








13-5 








108 








E. V. 


L. I. 8. 


L. I. 8. 




12-3 


14-2 


14-8 




13-7 


14-11 


16-0 




110 


106 


109 




E. V. 


L. W. 


L. I. 8. 


L. I. 8 


13-11 


14-11 


15-4 


15-10 


14-8 


15-3 


17-2 


17-8 


105 


102 


112 


112 


L. W. 


L. I. S. 


L. I. 8. 




6-6 


7-5 


8-0 




6-6 


7-8 


9-3 




100 


103 


lie 




L. I. 8. 








12-0 








12-9 








106 








L. I. 8. 








11-2 








11-5 








102 








L. I. 8. 








11-1 








11-8 








105 








E. V. 


L. I. S. 


L. I. 8. 




13-3 


14-9 


15-3 




14-1 


15-0 


15-10 




106 


102 


104 




L. W. 


L. I. S. 


L. I. 8. 




6-11 


7-6 


8-0 




7-3 


7-7 


8-5 




104 


101 


105 




L. I. S. 








8-10 








8-8 








98 








L. I. 8. 


L. I. 8. 


L. I. 8. 




8-10 


9-3 


9-10 




8-4 


9-2 


9-8 




94 


99 


98 




E. V. 


L. I. 8. 


L. I. S. 




12-0 


13-10 


14-4 




11-8 


13-1 


14-3 




97 


95 


99 





MENTAL GROWTH CURVE 29 



TABLE VI— Continued 
Original Data Arranged in Order of Mean I. Q. — Boys 



71. Average I. Q. 96.0. 

Examiner E. V. E. V 

Chronological Age 12-2 13-9 

Terman Age 11-8 13-3 

I- Q. - 99 96 

7!. Average I. Q. 95.0. 

Examiner E. V. 

Chronological Age 11-2 

Terman Age lO-l 

I. Q 90 

73. Average I. Q. 93.2. 

Examiner E. V. 

Chronological Age 12-a 

Terman Age . ii-o 

I. Q- - 88 

74. Average I. Q. 93.2. 

Examiner E. V. 

Chronological Age 8-7 

Terman Age ... 8-2 

I- Q - 95 

75. Average I. Q. 92.0. 

Examiner L. W. 

Chronological Age 10-8 

Terman Age 10-2 

I. Q — 95 

76. Average I. Q. 92.0. 

Examiner E. V. L. I. S 

Chronological Age .- 9-5 11-11 

Terman Age 8-0 11-2 

I. Q 90 94" 



E. V. 








12-9 








12-9 








100 








E. V. 


L. I. S. 


L. I. S. 


L. I. 


14-1 


15-1 


15-6 


1&-0 


13-1 


14-7 


14-7 


15-5 


92 


96 


94 


9& 


L. W. 


L. I. S. 


L. I. S. 




10-0 


10-8 


11-2 




9-3 


9-8 


10-7 




92 


91 


95 




L. I. S. 








11-5 








10-2 








89 









the I. Q. occur. In order to illustrate this more completely the 
36 children of the Five Examination Group were arranged in the 
order of merit on the basis of the I. Q. for the first examination. 
For all of the children the first I. Q. was plotted, Chart Via and 
b, and the points connected by a solid line to show this array of 
children in the original order of increasing I. Q. The vertical 
scale represents the range of I. Q.'s from 80 to 100. The numbers 
running horizontally across the chart are the identification num- 
bers of the children in the tables of original data. The four suc- 
ceeding I. Q.'s for each child were plotted on the same vertical 
axis as the point for the first I. Q. and different kinds of lines 
drawn in order to make it possible to identify the I. Q. 's of dif- 
ferent children at the 2d, 3d, 4th and 5th examinations. The 
heavy horizontal lines indicate the conventional classifications of 
I. Q. level, 90 to 110 being considered average ability; 110 to 120 
superior, with an additional classification of very superior for 
120 to 140. In this study the very superior cases were not suf- 
ficiently numerous to permit of the last classification. Accord- 
ingly, all children with a mean I. Q. of 110 or above are classed as 
superior. 



30 



IOWA STUDIES IN CHILD WELFARE 



TABLE VII 
Original Data Arranged in Order of Mean I. Q. — Girls 



13. 



u. 



Average I. Q. 148.0. 

Examiner E. V. 

Chronological — 8-3 

Terman - 11-6 

I. Q. 139 

Average I. Q. 146.6. 

Examiner E. V. 

Chronological 8-11 

Terman 12-6 

I. Q. 140 

Average I. Q. 140.5. 

Examiner L. I. S. 

Chronological 8-10 

Terman 12-7 

I. Q -- -- 142 

Average I. Q. 131.7. 

Examiner E. V. 

Chronological 7-0 

Terman »S 

I. Q. 123 

Average I. Q. 130.7. 

Examiner E. V. 

Chronological -- 9-1 

Terman 11-3 

I. Q 123 

Average I. Q. 130.5. 

Examiner L. W. 

Chronological 6-4 

Terman 7-6 

I. Q. 118 

Average I. Q. 130.2. 

Examiner E. V. 

Chronological 9-6 

Terman 11-0 

I. Q 115 

Average I. Q. 130.0. 

Examiner E. V. 

Chronological 7-0 

Terman 9-2 

I. Q. — 131 

Average I. Q. 128.8. 

Examiner E. V. 

Chronological 8-10 

Terman 9-10 

I. Q. Ill 

Average I. Q. 127.8. 

Examiner E. V. 

Chronological 6-6 

Terman — 8-2 

I. Q 125 

Average I. Q. 125.5. 

Examiner E. V. 

Chronological 9-8 

Terman 10-3 

I. Q. - 106 

Average I. Q. 125.0. 

Examiner E. V. 

Chronological 8-9 

Terman 10-8 

I. Q. 122 

Average I. Q. 124.7. 

Examiner E. V. 

Chronological 4-11 

Terman 6-4 

I. Q. - 128 

Average I. Q. 124.6. 

Examiner E. V. 

Chronological — 10-9 

Terman 12-4 

I. Q 115 



E. V. 


L. W. 


L. I. S. 


L. I. S 


9^ 


10-4 


11-4 


11-10 


13-5 


16-4 


17-1 


17-7 


143 


158 


151 


149 


E. V. 


L. W. 


L. I. S. 


L. I. S 


10^ 


11-0 


12-0 


12-5 


13-11 


16-7 


18-7 


18-7 


139 


150 


155 


149 


L. I. S. 








9-7 








13-4 








139 








L. I. S. 


L. I. S. 


L. I. S. 




8-2 


8-8 


9-3 




10-5 


11-3 


13-6 




128 


130 


146 




E. V. 


L. I. S. 


L. I. S. 




10-2 


11-8 


12-2 




12-10 


15-10 


17-8 




126 


136 


138 




L. I. S. 








7-2 








10-3 








143 








E. V. 


L. I. S. 


L. I. S. 


L. I. S. 


10-7 


12-1 


12-7 


13-0 


13-7 


15-11 


17-8 


17-8 


128 


132 


140 


136 


E. V. 








8-1 








10-5 








129 








E. V. 


L. W. 


L. I. S. 


L. I. S. 


9-10 


11-1 


11-10 


12-4 


11-e 


15-5 


16-7 


17-1 


lie 


1S» 


140 


138 


E. V. 


L. I. S. 


L. I. S. 


L. I. S. 


7-5 


9-0 


9-6 


9-11 


9-2 


10-8 


12-9 


13-8 


123 


119 


134 


138 


L. W. 


L. I. S. 


L. I. S. 




10-e 


11-3 


11-10 




13-4 


15-1 


16-3 




125 


134 


137 




E. V. 








9-9 








12-6 








128 








L. W. 


L. I. S. 


L. I. 8. 




5-6 


6-6 


7-« 




6-10 


8-0 


8-8 




124 


123 


124 




L. S. 


L. I. 8. 






12-3 


13-S 






15-6 


17-8 






126 


133 







MENTAL GROWTH CURVE 



31 





Original 


Data 


TABLE VII- 
Abranged in 


—Continued 
Order of Mean I. 


Q.— Girls 


15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
2fl. 
27. 
28. 


Average I. Q. 


124.0. 


L. W. 


L. r. S. 

6-7 
8-0 
121 

L. I. S. 

6-9 
8-10 
131 

L. W. 

11-2 

12-11 

116 

L. I. 8. 
6^ 

7-6 
118 

E. V. 

9-10 
11-1 
112 

L. W. 
13-1 
16-4 
124 

E. V. 
7-6 
8-11 
119 

L. I. 8. 

8-3 
9-« 
115 

L. I. S. 
7-1 
9^ 

127 

E. V. 
8-11 
10-9 
120 

E. V. 

11-1 
12-3 
110 

E. V. 
11-fl 
13-1 
113 

L. I. 8. 

9-8 

11-2 

115 

L. I. 8. 

9-2 

10-8 

116 


L. I. 8. 
11-11 
15-7 
130 

L. I. 8. 
11-4 
12-3 
108 

L. I. S. 
14-1 

18-0 
128 

L. I. S. 

8-8 
10-10 
125 

L. W. 

10-5 

12-0 

115 

L. I. 8. 

12-6 
14-9 
118 

L. I. 8. 

1.3-0 

15-5 

118 

L. I. 8. 

10-0 

12-2 

121 

L. I. 8. 
9-7 
10-11 
114 


L. I. s. 

12-5 

16-11 

136 

L. I. 8. 
11-9 
15-3 
129 

L. I. 8. 
14-8 
18-6 
123 

L. I. S. 
5^3 
11-3 
122 

L. I. 8. 
13-0 
16-5 
126 

L. I. S. 

13-5 

17-2 

127 

L. I. 8. 
10-7 
13-0 
123 

L. I. 8. 
10-2 
12-2 
119 


L. I. 8. 

12-3 

17-8 

144 

L. I. S. 

13-6 

17-8 

127 

L. I. S. 
lS-11 
17-2 
123 


Chronological . 
Terman 




5-9 

7-4 


I. Q 




127 


Average I. Q. 

Examiner 

Chronological . 
Terman . 


123.5. 


.... L. W. 

5-7 
6-6 


I. Q 




116 


Average I. Q. 

Examiner 

Chronological . 


123.2. 


.... E. V. 

9-11 

11-0 


I. Q. 




111 


Average I. Q. 

Examiner 

Chronological . 

Terman 

I. Q 

Average I. Q. 

Examiner 

Chronological 


122.5. 
122.1." 


.... L. W. 

5-1 
6-6 
127 

.... E. V. 

8-9 
10-5 


I. Q. - 

Average I. Q. 

Examiner 

Chronological . 
Terman .. 


'i22"or" 


119 

.... L. I. S. 

11-5 
13-0 


I. Q. 

Average I. Q. 


'l2l"oy 


113 

E. V. 


Chronological . 

Terman 

I. Q. -— 

Average I. Q. 
Examiner .. _. 


'i26'5'"" 


6-1 

7-6 
123 

E. V. 


Chronological 
Terman . 




6^ 
8-0 


I. Q. 




120 


Average I. Q. 
Examiner 


120.0. 


L. W. 


Chronological . 
Terman 




5-11 




6-8 


I. Q. 

Average I. Q. 
Examiner 


"iig'or 


113 

E. V. 


Chronological 

Terman — 

I. Q. 

Average I. Q. 

Examiner 

Chronological . 
Terman 


'lisle"" 


7-10 
9-7 
122 

.... E. V. 

10-0 
11-3 


I. Q - 

Average I. Q. 
Examiner . 


"118^6"" 


112 
E. V. 


Chronological . 
Terman ... 




10-5 

11-5 


I. Q. 

Average I. Q. 
Examiner . 


'm'.i'.' 


109 

E. V. 


Chronological . 
Terman 




8-0 
8-10 


r. Q 




110 


Average I. Q. 
Examiner 


117.2. 


E. V. 


Chronological . 

Terman 

I. Q. 




7-7 

9-1 

120 



32 



IOWA STUDIES IN CHILD WELFARE 



TABLE VII— Continued 
Original Data Abeanged in Order of Mean I. Q. — Girls 



29. Average I. Q. 117.0. 

Examiner 

Chronological 

Terman 

I. Q. 

30. Average I. Q. 116.8. 

Examiner 

Chronological 

Terman 

I. Q. — - 

31. Average I. Q. 116.2. 

Examiner 

Chronological 

Terman 

I. Q. 

32. Average I. Q. 118.0. 

Examiner 

Chronological 

Terman 

I. Q - 

33. Average I. Q. 115.6. 

Examiner 

Chronological -— 

Terman 

I. Q. — - 

34. Average I. Q. 115.5. 

Examiner 

Chronological 

Terman 

I. Q 

35. Average I. Q. 114.5. 

Examiner 

Chronological 

Terman 

I. Q — 

36. Average I. Q. 113.5. 

Examiner 

Chronological 

Terman 

I. Q 

37. Average I. Q. 113.5. 

Examiner 

Chronological 

Terman 

I. Q. — - 

38. Average I. Q. 113.4. 

Examiner 

Chronological .- 

Terman 

I. Q. 

39. Average I. Q. 11'>.0. 

Examiner 

Chronological 

Terman .— 

I. Q. 

40. Average I. Q. 112.0. 

Examiner 

Chronological 

Terman 

I. Q. 

41. Average I. Q. 110.5. 

Examiner 

Chronological 

Terman 

I. Q - — 

42. Average I. Q. IIO.O. 

Examiner 

Chronological 

Terman 

I. Q. 



E. V. 


L. W. 


L. I. S. 


L. I. 8. 




5-7 


6-9 


7-8 


8-2 




6-6 


7-8 


&-0 


10-0 




116 


113 


117 


122 




E. V. 


E. V. 


L. W. 


L. I. S. 


L. I. S 


8-11 


10-3 


11-4 


11-11 


12-S 


10-7 


11-9 


12-1 


14-^ 


15-8 


118 


114 


106 


120 


126 


E. V. 


E. V. 


L. I. S. 


L. I. S. 




9-3 


10-9 


12-4 


12-10 




10^9 


12-5 


14-1 


15-5 




116 


115 


114 


120 




L. W. 


L. I. S. 








5-11 


7-2 








6-2 


&-2 








104 


128 








E. V. 


L. S. 


L. I. S. 


L. I. S. 


L. I. 8 


5-1 


6-1 


7-7 


8-1 


8-7 


5-0 


7-4 


9-2 


9-10 


10-2 


98 


120 


121 


121 


118 


L. W. 


L. I. S. 








5-4 


6-7 








6-6 


7-2 








122 


109 








E. V. 


L. W. 


L. I. S. 


L. I. S. 




9^ 


10-5 


11^ 


11-11 




10-10 


11-11 


12-10 


13-9 




116 


114 


113 


115 




E. V. 


L. W. 


L. I. S. 


L. I. 8. 




11-fl 


12-5 


13-1 


13-9 




12-6 


13-9 


15-1 


16-7 




108 


110 


115 


121 




E. V. 


E. V. 








6-1 


7-1 








6-10 


8-2 








112 


115 








E. V. 


L. S. 


L. W. 


L. I. S. 


L. I. S. 


6-2 


7-1 


8-9 


9-3 


9-8 


7-6 


8-4 


9-8 


10-3 


10-7 


121 


117 


110 


110 


109 


E. V. 


E. V. 


L. r. S. 


L. I. 8. 


L. I. 8. 


11-4 


12-11 


14-0 


14-4 


14-10 


11-6 


14-10 


14-10 


17-7 


17-7 


101 


114 


105 


122 


118 


E. V. 


E. V. 


L. W. 


L. I. S. 


L. r. 8. 


8-2 


9-3 


10-7 


11-2 


11-8 


*-4 


10-2 


11-2 


12-0 


14-7 


114 


109 


105 


107 


125 


L. W. 


L. I. S. 








6-8 


7-6 








7^ 


8^ 








110 


111 








E. V. 


L. I. S. 


L. I. S. 


L. I. 8. 




9-4 


10-7 


10-11 


11-6 




&-7 


10-€ 


12-3 


14-7 




10-2 


99 


112 


127 





MENTAL GROWTH CURVE 



33 









TABLE VII 


— Continued 






Original 


Data 


Arranged in 


Order of 


Mean I. 


Q. — Girls 


43. 
44. 

45. 
46. 
47, 
48. 
49. 
50. 
51. 
52. 
53. 
54. 
55. 
56. 


Average I. Q. 
Examiner 


109.0. 


E. V. 


E. V. 

8-10 

9-8 

109 

L. I. S. 

7-7 
8-7 
113 

E. V. 

9-9 

KM, 

105 

L. W. 

14-2 

15-6 

109 

L. I. S. 
10-:3 
10-8 

104 

L. r. s. 

9-9 
10-1 
103 

E. V. 
11-3 

12-3 
109 

L. W. 
7-11 
8^ 
105 

E. V. 

16-9 

18-0 

112 

L. I. S. 
7-4 

7-8 
105 

L. I. S. 

7-4 
7-10 
107 

L. I. S. 
6^ 
6^ 
lOO 

E. V. 

12-6 

13-0 

104 

L. r. S. 
6-9 
7-2 
106 


L. I. s. 

10-1 

10-7 

104 

L. W. 

11-0 

12-1 

109 

L. I. 8. 

15-3 

16-8 

109 

L. I. S. 

10-8 

11-6 

103 

L. I. S. 
8-3 
»^ 
112 

L. I. S. 

17-8 

18-0 

112 

L. I. S. 

13-10 

15-10 

114 


L. I. S. L. I. S. 

10-5 11-0 

11-10 11-10 

113 108 

L. I. S. 
15-9 

16-8 
106 

L. I. S. 

11-2 

11-9 

105 

L. r. s. 

9-3 
9-9 
105 


Chronological . 

Terman 

I. Q. - 

Average I. Q. 

Examiner 

Chronological . 
Terman 


"ios^s'" 


7-6 

a4 

Ill 

L. W. 

6-5 

6^ 


r. Q 




104 


Average I. Q. 

Examiner 

Chronological . 
Terman . 


108.0. 


E. V. 

8-8 

9-7 


I. Q. 

Average I. Q. 

Examiner 

Chronological . 

Terman 

I. Q — 

Average I. Q. 

Examiner 

Chronological . 
Terman 


'ios'o'" 

'i07"7'' 


110 

L. S. 

12-7 

13-8 
108 

E. V. 

8-11 

10-2 


I. Q — . 

Average I. Q. 

Examiner 

Chronological . 

Terman 

I. Q. ._ 


'irn's'.' 


114 

.— E. V. 
9-3 

7-0 
112 


Average I. Q. 

Examiner 

Chronological . 

Terman 

I. Q. 

Average I. Q. 

Examiner* 

Chronological . 
Terman 


107.5. 


- E. V. 

9-9 


"iwyo'' 


10-4 
106 

E. V. . 

6-7 

7-0 


I. Q. 




100 


Average I. Q. 
Examiner . . 


107.0. 


L. S. 


Chronological . 
Terman 




15-7 
15-3 


I. Q. . 




97 


Average I. Q. 
Examiner _- . 


106.5. 


L. W. 


Chronological . 

Terman 

I. Q. 

Average I. Q. 

Examiner 

Chronological . 
Term an . - 


loe'o' 


6-0 
6-6 

108 

-.-- L. W. 

6-6 
6-10 


I. Q. - - 

Average I. Q. 

Examiner 

Chronological . 

Terman 

I. Q. 


'iol'.h'." 


105 

.... L. W. 
5-1 

5-8 
111 


Average I. Q. 
Examiner .. .. 


105.3. 


E. V. 


Chronological . 
Terman 




11-3 
11-1 


I. Q 




98 


Average I. Q. 

Examiner 

Chronological . 
Terman 


101.5. 


.... L. r. s. 

6-0 
6-2 


I. Q. 




103 



34 



IOWA STUDIES IN CHILD AVELFARE 



TABLE VII— CoNTXNUEn 
Obiginal Data Arranged in Order of Mean I. Q. — Girls 



as 



57. Average I. Q. 103.5. 

Examiner 

Cbronologieal 

Terman 

I. Q. - 

58. Average I. Q. 102.7. 

Examiner 

Chronological 

Terman 

I. Q. — 

59. Average I. Q. 102.6. 

Examiner 

Chronological 

Terman 

I. Q 

60. Average I. Q. 102.5. 

■Examiner — 

Chronological 

Terman 

I. Q. — — - 

01. Average I. Q. 102.5. 

Examiner 

Chronological -- -. 

Terman 

I. Q. — - 

62. Average I. Q. 98.5. 

Examiner 

Chronological 

Terman 

I. Q. 

Average I. Q. 93.8. 

Examiner 

Chronological 

Terman 

I. Q - 

Average I. Q. 93.5. 

Examiner 

Chronological 

Terman 

I. Q. 

Average I. Q. 92.7. 

Examiner 

Chronological _.. 

Terman 

I. Q. 

Average I. Q. 91.7. 

Examiner 

Chronological 

Terman 

I. Q. 

Average I. Q. 91.5. 

Examiner 

Chronological 

Terman _.. 

I. Q 



66. 



67. 



E. V. 


E. V. 


L. I. 8. 


L. I. S. 




8-8 


9-8 


11-8 


12-3 




9-8 


10-5 


11^ 


12-2 




111 


107 


97 


99 




E. V. 


E. V. 


L. I. S. 


L. I. S. 




9-2 


10-3 


12-3 


12-9 




9-8 


10-9 


12-0 


13-3 




105 


104 


98 


104 




E. V. 


E. V, 


L. I. S. 


L. I. S. 


L. I. S 


7-11 


9-0 


10-7 


10-11 


11-5 


8-2 


9-9 


10-3 


10-9 


12-4 


108 


108 


96 


98 


108 


E. V. 


L. I. S. 








12-6 


14-10 








ia-0 


14-11 








104 


101 








L. W. 


L. I. S. 








&-3 


9-3 








8-4 


9-7 








101 


104 








L. W. 


L. I. S. 








5-4 


fJ-6 








5-2 


6-6 








97 


100 








E. V. 


E. V. 


L. I. S. 


L. I. S. 


L. I. S 


9-6 


10-4 


11-e 


11-11 


12-6 


8-8 


10-4 


10-7 


10-10 


11-10 


91 


100 


92 


91 


95 


E. V. 


E. V. 








9-8 


10-7 








8-10 


10-2 








91 


98 








E. V. 


L. W. 


L. I. S. 


L. I. S. 




6-4 


7-7 


8-4 


8-11 




5-10 


7-0 


7-9 


8-5 




92 


92 


93 


94 




E. V. 


L. W. 


L. I. S. 


L. I. S. 




9-3 


10-^ 


11-0 


11-6 




9-4 


9-6 


9-9 


10-2 




100 


90 


89 


88 




L. W. 


L. I. S. 








11-2 


12-3 








9-8 


11-9 








87 


96 









It is apparent that these class names have very little real sig- 
nificance, as almost all of the children vary from their original 
classfiieation on re-examination, A variation of only a few points 
in the I. Q. measuring actual mental growth or occurring as a 
chance error of examination would be sufficient to transfer a child 
from the average to the superior class. The same amount of vari- 
ation might keep a child within its class if the original I. Q. has 
been sufficiently low. This fallacy in the use of type names has 



MENTAL GROWTH CURVE 35 

long been recognized by careful students of individual difeerences 
but it needs to be emphasized again because of the loose use of 
these terms by "Binet testers." 

Inspection of the variations in each child's I. Q. as shown m 
Chart VI shows that the original I. Q. is only approximately con- 
stant upon successive examinations. In two cases the second, 
third fourth and fifth I. Q.'s are actually below the first I. Q. ; m 
five cases one of the later I. Q.'s is below the original one and m 
ten cases two or more of the later I. Q.'s are below the first The 
remaining 19 cases show a general increase in I. Q., though eacn 
succeeding examination does not always give a higher I. Q. than 

the one preceding. 

The uniform and homogeneous nature of the mean I. Q. curves 
in Chart IV tends to give a false impression of the individual 
child's successive I. Q.'s. For this reason the individual curves 
of the 36 children who had the largest number of examinations 
were plotted in Charts VII and VIII in order to show the actual 
variations in I. Q. that occur. A comparison of the charts for 
boys and girls shows a greater irregularity of development m 
girls together with a tendency toward greater decrease in I. Q. 
at the later ages, probably due to the fact that the girls, who are 
more advanced in their development, can not maintain their orig- 
inal rates because of having passed so many of the tests at the 
upper limit of the scale. The fairly consistent and uniform curve 
which would correspond to an absolutely stable I. Q. is not ex- 
emplified in any of the girls' curves and in only two of the boys 
curves, Nos.^ 3 and 17. A gradual steady increase in I. Q. is 
observable in some instances, as for example m the curves ot 
boys Nos. 25, 34 and 61 and girl No. 5. Examples of curves show- 
ing a steady rise followed by a decrease in I. Q. are: for boys 
Nos 11 and 8 and for girls Nos. 1, 7 and 26. Curves showing 
marked irregularities with the I. Q. alternately increasing and de- 
creasing are : for girls Nos. 63 and 39, and for boys Nos. 47 and 33. 
While many of these changes are well within the 5 point limit 
of safety, a sufficient number show deviations of such magnitude^ 
that extreme care should be exercised about making any dogmatic 
statements in regard to what a child's future status will be. For 



iThese numbers correspond to the number, assigned the children in the tables of 

"""'SrRoot^W. T. Two Cases Showing Marked Change in I. Q., /. 0/ A-ppl. Psychol., 
(5) 1921, i56-158. 



36 



IOWA STUDIES IN CHILD WELFARE 
CHART Via 



'111 



t40 



SUCCESSIVE I.Q.'S 
3 4 



~2«BRT>asr- 






A 



rA. Jl I ... 







example, Girl No. 9 (Chart VIb) whose I. Q. in the first test was 
111, obtained on four subsequent tests 116, 139, 140 and 138. A 
careful study of this case showed no difference in the method of 
examination and no unusual physical condition aside from the 
adolescent physiological acceleration. 

No doubt these fluctuations in general mental achievement were 
modified more or less by such factors as time of day, health con- 
ditions at the time of the examination, fatigue, interest of the 
child in a particular examination, and changes in the home and 
school environment. Similarly conditioned changes in attitude 
on the part of the examiner might also have their effect. 

2. Deviations of Individuals from their Mean I. Q. Level. In 
order to determine other causes of the variability that is apparent 
from an inspection of the individual I. Q. curves, each child's 
deviation in I. Q. for every examination was calculated from his 
mean I. Q. in all of his examinations. For example, one boy of 
very superior general intelligence showed on 5 examinations, 
deviations of -\-.4, — 1.6, — 1.6 and -f-3-4; another boy of average 
ability showed very different deviations. It is possible that these 
deviations are influenced by chance errors of examination. Never- 
theless it is apparent that the size of these deviations depends not 
only on the real (inherent) variability of the child, but also upon 
the size of his mean I. Q. A large deviation on a high I. Q. may 



MENTAL GROWTH CURVE 
CHART VIb 



37 



leo 



T 



T-^-ff^ 






6"*' 



ISO 




90 



6|23 SiM Bia GiJO GilS Bi(2 dJa ei39 B|20 Bil? Bill ei5 GilO BiS a^ Gii G|2 BiJ 

not be very different from a small deviation on a low I. Q. In 
order to make all deviations comparable they were expressed as 
percentages of each child's mean I. Q. These percentages were 
then averaged for each child and the mean of the individual 





TABLE VIII 


Mean of Individtjal Deviations From Intelligence Quotient Level 




Boys 


Girls 




Mean P. E. 


Mean P. E. 


Superior I. Q. 110 + 


4.48 .53 


6.92 .78 


Average I. Q. 90-110 


2.65 .23 


3.80 .29 


Total 


3.99 .38 


5.95 .57 


Under 10 at last exami- 






nation 


3.60 .31 


5.14 1.19 


Over 10 at first exami- 






nation 


4.85 1.26 


7.09 1.36 



variabilities obtained for various classes of subjects (Table VHI). 
The mean for all the boys was 3.99 ± .38; for all of the girls 
5.95 ± .57. The mean for the superior boys was 4.48 ± .53, for 
superior girls 6.92 ± .78. The mean for average boys was 2.65 ~ 
.23 ; for average girls 3.80 ± .29. 

To determine whether chronological age was also a factor tend- 
ing to make the individual vary from his I. Q. level, means were 
obtained for boys and girls who were under 10 years of age at 



38 



_1«L 



10 WA STUDIES IN CHILD WELFARE 
CHART VII 

\ f n \ \ \ \ — ! — r — T 



rWDIVHJUAL 1.0 




the last examination and for those over 10 at the first examina- 
tion. The mean for the boys who were under 10 years of age at 
their last measurement was 3.60 ± .31 ; for boys who were over 
10 at their first measurement was 4.85 ± 1.26. The mean for girls 
who were under 10 years of age at their last measurement was 



CHART VIII 




•d 



i -f ^ ^ tb ik lb 1^3 ik i!s 



ACr M YFiUrS 



MENTAL GROWTH CURVE 



39 



5.14 ± 1.19 and for those over 10 at their first measurement was 
7.09 ± 1.36. 

The P. E. of all these means is sufficiently large to obscure the 
difference between the means for the group under comparison. 
There is, nevertheless, a constant tendency in all the groups for 
the girls to be more variable than the boys, for the superior chil- 
dren to be more variable than the average children and for the 
older children to be more variable than the younger, 

3. Differences in I. Q. at Successive Examinations. One method 
of studying the stability of the I. Q. is that of direct observation 
of the changes that take place on re-examination. For every pos- 
sible combination of examinations in the four groups the differ- 
ences of I. Q. for each child were computed and the increases in 
I. Q. tabulated as positive and the decreases as negative. These 
positive and negative variations were then grouped by class in- 
tervals of 5 point differences in I. Q. and the per cent of cases 
showing each amount of difference calculated. For example, 16 
of the 74 boys who had two examinations showed a decrease of 
to 5 points on the second examination; i. e., 21.6% showed this 
amount of negative difference. The percentage distribution of 
the differences, exclusive of the cases showing no differences, is 
shown for boys and girls in Table IX and Chart IX. 

Between the first and second examination the percentage dis- 
tribution of differences approximates the normal frequency curve 
with the greatest number of cases showing a positive change 
within the 5 point range. As the interval between examinations 
increases the effect of the repeated examinations intervening be- 
comes apparent in a shift toward the positive end of the scale. 
Although there is no large sex difference, the girls have a wider 
range of deviation, particularly those of the Four and Five Exam- 
ination Groups, where the last examination fell for the majority 
of the children within the period of adolescence. 

The mean change in I. Q. was found to be 



Examination 


1-2 


2-3 


3-4 


4-5 


Deviation 


- + 


— + 


— + 


— + 


Boys 
Girls 


4.61 7.39 
4.53 7.32 


5.12 7.00 
5.17 8.00 


3.42 7.27 
3.75 6.79 


2.50 5.14 
3.44 7.75 



Here there is evident a shift in the relation between negative 
and positive changes as the number of examinations children have 
taken grows larger. 



40 



IOWA STUDIES IN CHILD WELFARE 











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rH rH Ol C-l CO CO 


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i 



MENTAL GROWTH CURVE 
CHART IX 



41 













Percentage Distribution 

oS the 
DlFfERENCEe IN I Q 












ooys 




i7/r/3 1 






l-2l' 


xam. 


























20 





















— ^ 





















































2-3 Li 


xam 










































_^ 














-^ 















































20 




3-4 L 


xarr>, 














































1 





















































40 




4-5 t 


xom. 


































v>*-0 














































































1-3 L 


mm 


- 


























"^20 




u 








t=d 





























2-4 1 


nam 




























"^20 















































































40 
20 






3-5 I 'xom 








































H 


1 










■ 1 







40 






























"" 




l-A 


txom 




























20 




o 





































AO 
XO 






2-5 


Dxom 










— 




















































40 




































IS 


i'xam 




























20 
O 












1 


— 





















- 



■SO 



-20 



-10 



O +10 +20 +30 +40 

Amount of Difference 



+SO 



42 



IOWA STUDIES IN CHILD WELFARE 



These I. Q. changes cannot, however, be taken at their face 
value, since a large change on a high I. Q. may not be more signif- 
icant than a small change on a low I. Q. In order to make all 
changes comparable, the mean gains and losses from the first 
to second, second to third, third to fourth, and fourth to fifth 
examinations were expressed as per cents of the mean I. Q. at the 
1st, the 2d, the 3d or the 4th examination, depending on the com- 
parison being made. The material was also arranged to give a 
separate mean for average and superior children. The per cents 
of change in I. Q. follow : 



Examination 


1-2 


2-3 


3-4 


4-5 


Deviation % 

Superior 

Boys 




+ 


— 


+ 


— 


+ 


+ — 


4.3 


7.0 


5.1 


6.5 


3.1 


7.5 


2.0 4.2 


Girls 


3.5 


8.5 


3.5 


7.1 


4.1 


5.8 


2.5 6.3 


Average 
Boys 


3.9 


5.0 


3.0 


6.5 


2.3 


4.8 


1.9 


Girls 


5.0 


5.5 


6.8 


6.3 


2.9 


5.7 


5.0 7.0 



This tabulation shows a slightly greater per cent of change, 
especially in the positive direction, for superior children, due 
probably to the fact that superior children profit more readily 
by practice. 

It would be of great interest to know what is the effect of 
chronological age upon the change in I. Q., but the writers have 
been unable to devise any reliable method of determining the 
facts from the data available. The computation of the mean I. Q. 
change at each chronological age is not permissible because of 
the varying amounts of practice. For example, at age 8 there 
are the first examinations for some children, and also the second, 
third, fourth and fifth for others. Such tabulation of cases with 
reference to the age at the first test would, moreover, class the 
children whose second examination was given after a consider- 
able time, with those who had been re-examined at a shorter in- 
terval, and would tend to obscure any characteristic chronological 
changes occurring. It would seem that the question of whether 
older children show a different amount of I. Q. change than 
younger children could be solved only by a special experi- 
ment with a series of examinations beginning at a uniform age, 
on children of equal intelligence, and applied at uniform intervals. 

No determination can be made in this study of the effect of the 
interval separating the examinations. The change from the 1st to 



MENTAL GROWTH CURVE 43 

the 5th I. Q. cannot be compared with the change at other intervals 
because of the different amounts of practice intervening. 

Terman (26) 1919, p. 138, used the method of I. Q. comparison 
described as follows : 

"Tests have been given to 315 children in the vicinity of Stan- 
ford University, To 46 of these children, three or more tests 
have been given. In case of a child tested several times each test 
has been compared with each of the others, for example, the first 
test with the second, third, and fourth, separately, the second 
test with the third and fourth separately, and the third test with 
the fourth. This gives in all 435 I. Q. comparisons." 

Terman (26) p. 140, reports that his comparisons show: "that 
it makes little difference whether the child was bright, average 
or dull, how long an interval separated the tests or w^hat the age 
of the child was at the earlier test. The majority of the changes 
are for all groups relatively small .... 

"The central tendency of change is represented by an increase 
of 1.7 in I. Q. : the middle 50% of change lies between the limits 
of 3.3 decrease and 5.7 increase; the probable error of a predic- 
tion based on the first test is 4.5 points in terms of I. Q." 

The method of I. Q. comparison as used by Terman is open to 
the objections stated above. The I. Q.'s obtained after repeated 
examinations are pooled with those from a first examination, and 
the average tendency of change computed on the basis of these 
data. It seems to us that the differences in practice would make 
it inadvisable to pool these examinations. 

Such a tabulation of change in I. Q. with reference to the age 
at the first test would, moreover, afford no opportunity for the 
special characteristics of the adolescent period to show them- 
selves if they existed. As has been demonstrated in connection 
with the mental growth curves, and the physical growth curves, 
boys and girls have a period of adolescent acceleration at differ- 
ent chronological ages, and children of superior and average 
mental and physical status show a similar difference. A pooled 
classification of these different classes of data tends to destroy 
any characteristic chronological age changes in I. Q. 

We have felt that the solution of these proolems would not be 
obtained by the use of this method. The 695 separate I. Q. com- 
parisons afforded by the data in this study would have been re- 
duced to a very small number if the comparisons had been made 
only with children of the same chronological age, sex, I. Q. level, 
and physical status. 

4. Intercarrelations. The stability of the I. Q. can be investi- 



44 IOWA STUDIES IN CHILD WELFARE 

gated by another means than that of noting the size of the differ- 
ences in I. Q. and calculating the central tendency of change. 
The similarity in the relative rankings of children on successive 
examinations can best be studied by means of the method of cor- 
relation. Although several writers have reported correlations 
between two examinations no data have so far been presented in 
the literature to show the intercorrelations of several examina- 
tions given on the same group of children for several years. From 
such an array of correlations one can determine whether the ma- 
jority of children maintain at a later examination their relative 
position above or below the mean of their group and tend to 
deviate from this mean by approximately the same amount after 
several years interval. The accuracy of the prediction is condi- 
tioned by the size of the correlations. A high correlation between 
the I. Q.'s obtained by a group of children on two examinations 
would mean considerable stability in I. Q. and the possibility of 
predicting with a high degree of accuracy the future status of 
children of any I. Q. level. 

For this method of investigating the evenness of the mental 
growth there were calculated Pearson coefficients of correlation 
for four groups of children. One group consisted of 56 children 
who had been examined twice; the coefficient of correlation for 
the two examinations was -f-.81±.03. Another group consisted 
of 51 children who had been examined three times ; the coefficient 
for the first and second was -\-.1Q-.04l; for the first and third 
-I-.69 ± .05 ; for the second and third +.83 ± .03. 

It was possible to give a fourth examination to all but 9 of 
this group. The coefficients for this smaller group were, for the 
first and second examinations -l-.79±.04, for the second and third 
+.86 ± .03, for the third and fourth +.93 ± .02, for the first and 
third +.77 ± .04, for the second and fourth +.82 ± .03, and for 
the first and fourth +.72 ± .05. 

The last group of 36 children was given five examinations. 
The correlation between the first and second was +.85±.03, 
between the second and third +.85±.03, between the third and 
fourth +.91±.02, between the fourth and fifth +.92±.02, be- 
tween the first and third +.74±.05, between the first and fourth 
+.78±.04, between the first and fifth +.82±.04, between the second 
and fourth +.80±.04, between the second and fifth +.82±.04, and 
between the third and fifth +.84±.03. 



MENTAL GROWTH CURVE 



45 





TABLE X 


iNTBaiCOKBELATIONS OF InTEIXIGENCE QUOTIENTS FOR TWO, THREE, FoUR AND 

Five Examination Groups 


Examination 


1 

and 

2 


1 

and 

3 


2 

and 

3 


1 

and 

4 


2 

and 

4 


3 

and 

4 


1 

and 

5 


2 

and 

5 


3 

and 

5 


4 

and 

5 


5 Exam. Group.-JCoef 

IF. E 


+ .85 
±.03 


+ .74 
±.05 


+ .85 
±.03 


+ .78 
±.04 


+ .80 
±.04 


+ .91 
±.02 


+ .82 
±.04 


+ .82 
±.04 


+ .84 
±.03 


+ .92 
±.02 


4 Exam. Group.-JCoef 

IP. E 


+ .79 
±.04 


+ .77 
±.04 


+ .86 
±.03 


+ .72 
±.05 


+ .82 
±.03 


+ .93 

±.02 










3 Exam. Group.. JCoef 

^P. E 


+ .76 
±.04 


+ .69 
±.05 


+ .83 
±.03 
















i Exam. Group. .$Coef 

IF. E 


+ .81 
±.03 





















The coefficients (Table X) are uniformly high and reliable with 
low probable errors, ranging from +.72 ± .05 to +.93 ± .02. The 
coefficients of correlation for near-lying examinations, that is, 
two examinations with none intervening, are highest, the mean 
being +.88. For three correlations with one intervening exam- 
ination the mean is +.79. For the two with two intervening 
examinations the mean is +.80, and for the one with three interven- 
ing examinations the correlation is +.82. Although the coefficient 
is highest for near-lying examinations there is no tendency for the 
correlation to decrease with increase of interval. 





TABLE XI 
Percentage of Children Tested by 


Same Examiner 




Group 


Examiner 


■a «3 
a X 


•V 3 
a y. 


c 
a X 


rs OS 
a y, 

03 ^ 
iH 


73 03 

a y. 

03« 


a y 
e<3 


T o: 
c y. 


«5 
a y. 


a y 


la g 

-O o! 

a y 
03 pq 


5 Exam 

4 Exam 

3 Exam. 

2 Exam. 


E. V 


91.4% 







8.6 

32.2 




S9.8 

77.8 






•'•> 2 


0% 



100 





100 





100 


0% 



lOO 






18.6 
81.4 





100 


0% 



lOO 





100 


0% 



100 






18.6 
81.4 


0% 


40 

60 





lOO 



0% 



100 


0% 



100 


0% 





40 
60 


0% 


100 



L. S. 


L. W 

L. I. S — 

Misc 


E. V 

L. S. .- 


L. W 

L. I. S 

Misc. 


E. V 


L. S 


L. W 

L. I. 8 


E. V 


28.6 





3.5 

67.8 


L. S 


L. W 

L. I. S. 

Misc. .— 





46 IOWA STUDIES IN CHILD WELFARE 

It is possible that the size of the correlation might be influenced 
by the fact that a number of children were examined on both oc- 
casions by the same examiner. A study of Table XI shows that 
although for the two highest coefficients +.93 and +.92, 100% 
of the examinations were made by the same examiner, the next 
highest coefficient, +.91, showed only 40% by the same examiner. 
Other high coefficients are +.86 with 18.6% of the examinations 
and +.85 with 91.4%) of the examinations by the same examiner. 
A correlation of +.85 was also found where no child had been 
examined twice by the same examiner and a coefficient as low as 
+.76 was obtained with 17.8% of the examinations made by the 
same examiner. It would appear then that the personal equation 
of the examiner although of some influence is not the important 
factor in the size of the correlation. 

In general it is not justifiable to compute correlations for a group 
with such a wide range in chronological age. Such a procedure 
would tend to raise the correlation. The correlations between I. 
Q.'s are probably not subject to criticism from this point of view, 
since the I. Q. compensates for the difference in the chronological 
ages. 

Considerable doubt has been thrown by K. Pearson (Proc. Roy. 
Soc, 1897 (60) 489.) on the justifiability of correlating ratios. 
From this point of view the calculation of correlations between I. 
Q.'s may result in spurious correlation. This method is, however, 
the only feasible one at this stage in the development of the 
problem. 

In each group the highest correlations occur between near-lying 
examinations at the end of the series of examinations where the 
children were better adjusted to the situation and had apparently 
reached a certain stability of position within the group. 

For comparison it is of interest to note the size of the correla- 
tions obtained by other examiners. These were: Bobertag, +.95 
(Binet) ; Terman, +.93 (Stanford) ; Cuneo and Terman, +.95, 
+.94, +.85 (Stanford) ; Rosenow, +.82 (Binet and Stanford) ; 
Rugg and Colloton, +.84 (Stanford). 

5. Prohable Error of Estimate. Knowing the value of the 
coefficient of correlation between the first and any succeeding test, 
we can predict what any future I. Q. would be and compute the 
difference between the I. Q. as predicted and as actually obtained, 
or the error of estimate. 



MENTAL GROWTH CURVE 



47 





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. 






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■a© ^ 



g2SSg^S8Sg2 5gggeggSgSSg82 8gg8SSSe8SS 






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1^ '2 . 

•w" g 5 -O o (^ 
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2gSgS8gS8288^^8e8888J§S82S88gSe§2S8S2 

in ^•'i-H lOXCC ^^ (MOO '<r9C>Oi-'CO-^*t^TPlo"^*lCC>t^'rH'c> 



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li-i^r-i-irHrtMWlMe-Jc 



IN N 4^ (M 41 « M £0 « M r; ! 



48 



IOWA STUDIES IN CHILD WELFARE 



Our data for five consecutive examinations of 36 children have 
been used to make a comparison of the I. Q.'s actually obtained 
and the I. Q.'s predicted by means of the regression equation: 

where y^ = the I. Q. to be predicted, y = the mean of the obtained 
(later) I. Q.'s, x = the mean of the obtained first I. Q.'s, x^ = 
the individual I. Q. on the first test, and o- = the standard devia- 
tion of the X or y series. 

The equation can more conveniently be used in the simplified 
form: 

y^=r-^^(x^)-^(j~rj^ i), 

The quantity j- zr is a constant through a whole prediction 

series, a different constant being used for each of the four pre- 
diction series (second, third, fourth and fifth I. Q.'s from first 

I. Q.'s). The quantity^ _ |. -?- ^^-is also a constant in each of 

X 

these four prediction series, which reduces the formula to i/i= 
^(^i)+^i' For example, by substituting the constants for the 
prediction of the second I. Q. one obtains yj=J8{x^)-\-29.5. For 
the prediction of the third from the first I. Q. : y^=.90(xi)-^15.9. 





TABLE XIII 




DlSTEIBUnON OF DiFFF.RKNCES BETWEEN OBTAINED AND PREDICTED I 

(Errors of Estimate) 


. Q.'s 


Examination 


2 


3 


4 


5 


Amount of 

I. Q. 
Difference 


Number of Cases 


0-5 


—9 


-fl2 


—6 


+6 


—7 


+4 


—10 


+7 


5-10 


—4 


+ 7 


—6 


+5 


—7 


+ 8 


— 6 


+7 


10-15 


—2 


+ 1 


—2 


+5 


—3 


+3 


— 2 


+2 


15-20 


1 





—3 


+ 2 


—1 


+ 2 


— 1 





20-25 








—1 





—1 








+ 1 



MENTAL GROWTH CURVE 
CHART X 



49 





^^^•m 




' 1 ' 


















Dt5TRI3UTI0N OF DIFFERENCES 
BETWEEN 

Obtained and Predicted IQ^s 












^th. £.x.am 


























































































4 th LKom, 
































































































3 rd Ekqit) 




























































































! 




Znd Exam., 














i 
























J 



-iO '£5 'ZO ~/S -10-5 -^3 -t-IO +15 +20 +£S +30 

Amoun f of Di/feren c e 
For the prediction of the fourth from the first I. Q. : y^ 
.90 (a; J +20.1. For the prediction of the fifth from the first I. Q. : 
2/,=.91(xJ+21.7. 

By the use of this formula the second, third, fourth and fiLfth 
I. Q.'s for each child were predicted and the differences between 



50 IOWA STUDIES IN CHILD WELFARE 

the predicted I. Q.'s and the I. Q.'s actually obtained at each of 
these examinations (the errors of estimate) calculated, together 
with the mean of the differences for the group as a whole. The 
I. Q.'s as actually obtained and as predicted are shown in Table 
XII. The distribution of the differences between obtained and 
predicted I. Q. 's is shown in Table XIII and Chart X. 

On the average the prophesied second I. Q. differs from the 
obtained second I. Q. by 4.7 points, P. E. ± .5, i. e., the chances 
are equal that the average for the differences between the pre- 
dicted and obtained I. Q.'s will not be less than 4.2 or greater 
than 5.4. The average difference between the predicted and ob- 
tained third I. Q. or the average of the errors of estimate is 8.5 ; 
between the predicted and obtained fourth I. Q. is 7.7 and be- 
tween the predicted and obtained fifth I. Q. is 6.3. The mean 
interval between the second and first examination was approxi- 
mately 13 months; between the third and first was 28 months; 
between the fourth and first was 36 months and between the fifth 
and first 41 months. 

While Table XII shows for each prediction series the most prob- 
able predicted I. Q. for each child, a better sampling from a larger 
number of cases might have resulted in another predicted I. Q. 
In other words, while 137.9 is the proper estimate for the second 
I. Q. for case 1, the probable error of estimate gives the number of 
points variation above or below this estimate that will take in 
50% of all the other possible estimates. Knowing the value of 
the 4 coefficients of correlation involved, one can calculate the 
probable error of estimate for each of the prediction series by 
means of the formula P. E. = .6745 X o- var. V 1 — r-. This for- 
mula gives as a probable error of estimate for the prediction of 
the second from the first I. Q. ±4.2, for the prediction of the third 
from the first I. Q. ±7.0 ; for the prediction of the fourth from the 
first I. Q. ±6.2 ; for the prediction of the fifth from the first I. Q. 
±5.5. The P. E. of estimate of the second from the first is ±4.2 
as previously stated, i. e., the chances are equal that the true 
predicted second I. Q. will not vary from the calculated I. Q. by 
more than ±4.2. The chances that the true predicted I. Q. will 
not vary from the calculated I. Q. by more than ±8.4 (or 2 P. E.) 
are 1802 in 10,000 or 1 chance in every 4.5. The chances that the 
true predicted I. Q. will not vary from the calculated by more 
than ±12.6 are 434 in 10,000 or the chances that a deviation 
greater than ±12.6 would occur are 1 in 22. The same chances of 



MENTAL GROWTH CURVE 51 

error per 10,000 on 2 P. E. and 3 P. E. exist for the other predic- 
tion series, the only difference in each case being the size of the 
P. E. The P. E. of estimate for the second examination is very 
nearly the same as that reported by Rosenow (20) which was 
3.988. 

The size of the P. E. obviously depends on the size of the co- 
efficient of correlation for the particular comparison involved. 
At first thought one might expect that an increase of interval be- 
tween the examinations would result in a larger error of estimate. 
An increase in the probable error of estimate was, in fact, ob- 
served to take place in the prediction of the third from the first, 
where the interval was lengthened by one year. As was noted 
in connection with the correlations, however, the coefficient does 
not decrease regularly with an increase of the interval, but re- 
flects the general habituation and improvement that has taken 
place and the tendency for each individual to find and remain at 
his characteristic level. 

The calculation of the regressions and of the probable errors 
of estimate is of no special significance for this particular group, 
since the later I. Q.'s are already known. The real value of the 
procedure lies in utilizing the knowledge in regard to the corre- 
lation between earlier and later examinations for predicting the 
later I. Q. of other children who have received only the earlier 
examination. Chart X shows there is a conspicuous increase in 
the positive and a decrease in the negative differences observable 
where the group has had considerable opportunity for becoming 
adjusted to the examinations. It is not possible from the data at 
hand to make an exact determination of the amount of error of 
prediction for various intervals of examination since all of the 
children in this group have had repeated measurements in be- 
tween, which influences the size of the correlations for the longer 
intervals. In order to determine how accurately one may pre- 
dict a child's I. Q. one year later, two years later, etc., the corre- 
lations will have to be obtained on a sufficient number of children 
at each examination interval without intervening practice. In 
the absence of such long-time data, one can say that it is possible 
to predict a child's I. Q. with a probable error of from 4 to 7 
points. Larger amounts of error would of course occur at the 
extremes of distribution. That such extreme variations do occur 
is shown by numerous cases in Table XII ; for example in the 



52 IOWA STUDIES IN CHILD WELFARE 

case of number 10, a difference of 23.2 exists between the pre- 
dicted and obtained third I. Q. 

The concept of a stable I. Q. involves a supplementary concept 
of a sort of initial acceleration or impetus of mental growth 
which predetermines the rate and level at which mental progress 
takes place and results in an approximately constant I. Q. The 
intelligence quotient could not, however, remain constant if 
serious fluctuations in the individual's rate of mental growth 
occurred. 

If it should be proven that at certain ages children normally 
grow at an increased rate, the usefulness of the I. Q. would be 
considerably limited. It would always be of value still in de- 
termining the relative mental status of children of the same age 
but it would lose much of its prestige as a convenient diagnostic 
instrument for predicting the status of a child at later stages of 
its mental growth. In a previous chapter we have shown that 
considerable fluctuation in the rate of mental growth occurs, 
notably a sharp rise in the mental age curve at the approach of 
adolescence. This general intellectual renaissance is apparently 
a function of physiological age, occurring earlier in girls than in 
boys and earlier in children of superior intellectual endowment 
than in those of merely average ability. The inevitable result 
of this phenomenon is an increased I. Q. which in many cases 
could not have been predicted from the child's intellectual status 
at an earlier age and which would be a very unsafe basis in 
certain instances for inferring at the age of puberty what his 
earlier I. Q. had been. Prediction would still be possible, however, 
if one had a complete knowledge of the normal irregularities in 
mental growth at different ages. 

Summary and Conclusions 

1. The tabulated results of individual cases show that the I. 
Q. is only approximately constant during successive examinations. 

2. Considering each child's deviation from his mean I. Q. ex- 
pressed as a per cent of his mean I. Q. there is a tendency for 
the girls to be more variable than the boys, for the superior chil- 
dren to be more variable than the average children, and for the 
older children to be more variable than the younger. 

3. Considering the difference between the first and second ex- 
amination the larger number of cases show a difference of less 
than five points ( — or +) in I. Q. ; between the first and other 



MENTAL GROWTH CURVE 53 

later examinations with intervening practice, many more cases 
show greater amounts of difference, the positive differences be- 
coming more and more marked. 

4. With the change expressed as a per cent of the previous 
I. Q. there is a slightly greater change in the positive direction 
for superior children, due probably to the fact that these profit 
more readily by practice. 

5. No final determination can be made of the effect of chrono- 
logical age or of the interval between examinations on the change 
in I. Q.'s. 

6. The coefficients of correlation between all examinations 
within the four groups are high and reliable, ranging from -f.72 
±.05 to +.93 ±.02, showing that they may be used as a basis for 
prediction. The correlations are probably only slightly modified 
by the personal equation of the examiners. 

7. The value of the probable error of prediction lies in utiliz- 
ing the knowledge in regard to the correlation between earlier 
and later examinations for predicting the later I. Q. of other chil- 
dren who have received only the earlier examinations. The P. E.'s of 
estimate range between 4.2 and 7.0 for the prediction of the 
second, third, fourth and fifth examination from the first, 

III. THE RELATION BETWEEN PHYSICAL AND MENTAL 

GROWTH 

1. Data. During the time that the psychological examinations 
were being made, physical measurements and x-ray photographs 
were taken with a view to analyzing the physical status and de- 
velopment of the children. A description has been given in an 
earlier study of the technique of taking the height and weight 
measurements and determining the area of the exposed surface 
of the carpal bones which serves as an index of anatomical de- 
velopment and is closely related to the physiological changes with 
their accompanying physical and mental phenomena. Mental 
measurements were also available for the children, some made 
on the same day as the physical examinations and others at vary- 
ing intervals with a few separated by as long a time as six 
months. 

2. Resemblances in the Mental and Physical Development of 
Brothers and Sisters. Among the children measured in the school 
in which our data were collected there happened to be a number 



54 



IOWA STUDIES IN CHILD WELFARE 



CHART XI 




A^g in Yiears 

who were related to each other. Chart^ XI shows the individual 
mental growth curves of two families in each of which three 
members had been given repeated measurements. Family A in- 
cludes a boy No.^ 3, and two girls, Nos. 2 and 20, two of whom 
are superior to the mean for the superior children of this study. 
Family B includes two boys, Nos. 10 and 40, and one girl, No. 39. 
These children are closer to the mean, and the girl is below it for 
a considerable part of its course. The members of Family A 
show a certain resemblance in the smooth and even rise of their 
gro-wth curves, whereas the curves for Family B are more irregu- 
lar and L. B. even shows periods of no measureable mental 
growth. There will be noted a similarity in the general trend 



^The norms on this chart are the mean for the superior and average children in thij 
study. 

-These numbers correspond to those assigned to individuals in the tables of original 
data. 



MENTAL GROWTH CURVE 



55 



of the mental growth curves of the brothers in Family B, and 
also of the sisters in Family A. 

3. Mean Mental Age of Physiologically Accelerated and Re- 
tarded Children. The children included in this study were di- 
vided into 4 groups on the basis of general physical development. 
Group 1 consisted of the boys whose height and weight were 
above the norms for their age, and Group 2 of the boys whose 
height and weight were below the norms, or very close to the 
norms in one or the other of these two measurements. Group 1 
consisted then of physiologically accelerated boys and Group 2 
of physiologically retarded boys, since it has been shown by Bald- 
win (1) and (3), that height and weight are closely correlated 
with physiological maturation. This division was made on the 
basis of the physical measurements without knowledge of the 
mental age of the child. A similar division into two groups was 
made for the girls. 

The corrected mental ages of the children in each of the four 
groups were then averaged for each chronological age as shown 
in Table XIV. The mean mental age of physiologically acceler- 



TABLE XIV 

Mean Mental Age in Months of Physiologic at,t,y Accelerated and 

Retarded Boys and Girls 


Chronological 

Age 


Boys 


Girls 


Accelerated 


Retarded 


Accelerated 


Retarded 


5 

6 

7 

8 

9 

10 

11 

12 

13 

14 


72.0 
89.4 
101.3 
118.2 
131.1 
142.4 
155.3 
171.1 
179.0 
194.2 


62.8 
83.2 
97.1 
110.8 
120.3 
131.0 
137.6 
150.1 
158.4 
166.2 


74.4 

81.3 

99.9 

114.6 

128.6 

141.1 

151.2 

176.7 

(182.5) 

194.9 


57.6 
79.0 
95.0 
10'7.0 
119.1 
131.0 
144.3 
168.2 
189.2 
183.7 



ated hojs is uniformly higher than the mean mental age of re- 
tarded boys. For the girls the same holds true with the exception 
of age 13, where the mean (printed in pt^renthesis) is too low 
because of the inclusion of the measurements of some girls who 
were of superior intellectual ability but of the very tall, thin type. 
This table confirms the findings of other investigators summar- 
ized in (2), who in general agree that superior mental develop- 
ment accompanies superior physical development as a rule. The 
first investigation to trace the correspondence between pedagog- 



56 IOWA STUDIES IN CHILD WELFARE 

ical acceleration and physical development by means of consecu- 
tive school marks and physical measurements was made by Bald- 
win (1) in 1914. The present study is the first to determine for 
the same individuals the relation between general physical status 
and mental growth as indicated by consecutive intelligence 
examinations. 

4. The Relation between Physical Traits and Mental Age. A 
correlation between height and mental age previously reported 
by Baldwin (2) was +.71^.04 for boys and +.62±.05 for girls. In 
the present study the particular mental age selected for each child 
was the one which had been determined nearest to the time of 
physical measurement. In no case was there more than a few 
months interval between the physical and mental measurement. 
The correlations obtained between height and mental age are for 
72 boys -f .84 ±.02, and for 61 girls -f .89 ±.02. The correlation 
between weight and mental age by Baldwin (2) was for boys 
+.68 ±.04 and for girls +.56 ±.06. In the present study the cor- 
relations for weight and mental age are higher, that is, for boys 
+.86±.02 and for girls +.77±.04. 

The significance of the growth of the carpal bones in rela- 
tion to general physical development was first emphasized by 
Rotch in 1910 and is summarized by Baldwin (3). In order to 
determine the relationship between anatomical age as indicated 
by the comparative development of the carpal bones and mental 
development as shown by the mental age rating, Pearson coef- 
ficients of correlation have been worked out by us. These coef- 
ficients give the first determination of the interdependence of 
these physical and mental traits. The coefficient of correlation 
between mental age and an index of anatomical age, (exposed 
area of the carpal bones of the right wrist) was for 54 boys 
+.873 ±.021 ; for 50 girls +.869 ±.023. 

Earlier correlations between height and weight and the exposed 
area of carpal bones for a group of children were reported by Bald- 
win (3). The correlations between height and total exposed area 
of carpal bones of the right wrist were for boys +.88 ±.03 and 
for girls +.73 ±.05. The correlation between weight and area of 
carpal bones was for boys +.76 ±.05 and for girls +.77 ±.05. For 
this study the correlations between height and weight for boys 
was +.92 ±.01, and for girls +.89 ±.02. 

As has previously been pointed out by Baldwin (2) the size of 
these coefficients is increased by the wide range of ages. It is 



MENTAL GROWTH CURVE 



57 



possible to gain some knowledge of the influence of the age factor 
by the method of partial correlation. The results for 49 girls 
selected because of the completeness of the data, show the follow- 
ing intercorrelations of height, weight, X-Rays, mental and chrono- 
logical age. 



TABLE XV 

Intebcoreelations Between Physical Teaits, Chronological and 

Mental Age 




Chr. Age 


Weight 


Height 


Mental Age 


Age 
Weight 
Height 
Mental Age 
X-Ray 


.84 
.88 
.88 
.92 


.86 
.71 

.88 


.89 
.92 


.83 



The partial correlations with one factor constant for these same 
girls are given in Table XVI. 



TABLE XVI 

PAETLU. COEEELATIONS BETWEEN PHYSICAL TBAITS, CHRONOLOGICAL AND 

Mental Age 


Traits 


Constants 


Chron. 
Age 


Mental 
Age 


Height 


Weight 


X-Ray 


Height-Weight 
Height-Chr. Age 
Height-Ment Age 
Height-X-Ray 
Weight-Chr. Age 
Weight-Ment. Age 
Weight-X-Ray 
X-Ray-Chr. Age 
X-Ray-Ment. Age 
Chr.-Ment. Age 


.57 

.53 
.62 

—.15 

.52 

.09 


.80 
.41 

.73 
.66 

.76 

.72 


.30 
—.40 
.37 
.62 
.04 
.47 


.52 

.81 
.65 

.71 
.63 
.76 


.38 
.16 
.59 

.14 
—.11 

.54 



The influence of chronological age is more important with some 
traits than others. For example the correlations between physical 
traits are very little influenced by keeping chronological age con- 
stant (+.89 to +.53). Although there is no correlation between 
weight or X-Rays and mental age for this group when chronolog- 
ical age is kept constant, there is a positive correlation between 
height and mental age. 



58 IOWA STUDIES IN CHILD WELFAKE 

Summary and Conclusions 

1. There is a similarity in the mental growth curves of broth- 
ers and sisters.^ The resemblance between brothers and sisters is 
further shown in physical traits by the correlation of the height 
X-Ray and weight quotients and in mental traits by the corre- 
lation between the I. Q.'s, The correlations are higher for the 
physical traits than for the mental. 

2. The mean mental age of physiologically accelerated is 
higher than the mean mental age of physiologically retarded chil- 
dren. This study is the first to determine for the same individuals 
the relation between general physical status and mental growth 
as determined by consecutive intelligence examinations. 

3. The coefficients of correlation between height and mental 
age are high even when the influence of chronological age is elim- 
inated. 

IV. GENERAL CONCLUSIONS 

For years the literature has been full of statements in regard 
to the desirability of obtaining repeated measurements on the 
same children in order to study the process of mental develop- 
ment. The use of the Stanford Revision of the Binet scale even 
for the relatively short period of four years shows the unsuita- 
bility of this scale in its present form as a means for measuring 
mental growth. The limited number of alternative tests results 
in a certain practice effect on repeated examinations. Another 
defect of the present system of tests is the lack of a sufficient 
number of tests at the higher levels to measure the mental growth 
that apparently goes on in a bright young child even after the 
exhaustion of the 16 or 18 year old tests. It is commonplace in 
clinical psychology that a gifted child has more opportunity to 
gain a high I. Q, if measured early in his life where he has a 
greater range of tests in which to succeed. Theoretically it would 
seem to be a better measure of mental growth to use a combina- 
tion of point scales for specific mental traits, each scale to be suf- 
ficiently extended to measure whatever ability exists and the whole 
system to include a sufficient variety of traits to afford a general 
measure of the development of the individual. 

The findings of this study have been summarized in detail at 
the end of each section. A survey of these results show the im- 
portance of many factors influencing mental growth processes, 



MENTAL GROWTH CURVE 59 

and producing differences in the mental growth curves of boys 
and girls, and of children of superior and average ability. 

An analysis of the individual growth curves shows^hat the I. 
Q. is only approximately constant during successive examinations. 
The amount of difference between I. Q.'s obtained at various ex- 
aminations is sufficiently small, and the correlations between the 
examinations are sufficiently high with small probable errors of 
estimate, to permit of predicting from an earlier examination 
what the individual's later development will be. 

The most significant outcome of this study is the empirical de- 
termination of the mental growth curve and the establishment of 
the close interrelation between mental and physical development 
as shown by the general similarity between growth in height and 
in mental age, the rise in the mental age curve at the adolescent 
years, the superior mental development of physiologically accel- 
erated children, and the high correlation between mental age and 
height. 

It is evident that mental age ratings by the present scale are the 
result not only of native intelligence but also of the degree of 
physiological acceleration over that which is normal for the age. 
This latter factor is of extreme importance in any educational or 
social treatment of the individual. A high I. Q. reflects this fac- 
tor as well as the general intelligence that it is designed to 
measure. 



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60 



MENTAL GROWTH CURVE 61 

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